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- Discussion Type
- discussion topicn-angulated category
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 28th 2012

- Discussion Type
- discussion topicCalculus is Topology
- Category Latest Changes
- Started by isomorphisms
- Comments 8
- Last comment by DavidRoberts
- Last Active May 28th 2012

- I recently came across some interesting ideas at inperc.com/wiki/index.php?title=Calculus_is_topology which might be incorporable into the nLab wiki -- although I'm not sure exactly where.

- Discussion Type
- discussion topiclectures on p-divisible groups
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 4
- Last comment by Stephan A Spahn
- Last Active May 27th 2012

I took some notes during my reading of (Chapters I-III of)

- Michel Demazure, lectures on p-divisible groups web

In the recent days I inserted parts of these notes in different nlab entries. Maybe it is of use to somebody to have all of these notes in wiki-form. So I created lectures on p-divisible groups containing the skeleton of the contents. I will fill in the parts I have written so far (roughly chapters I and II) tomorrow. Of course anyone should feel free to rewrite or complete the related entries. Currently the page names contain the chapter-numbering from the original text - I think this numbering can be discarded at the time the linked page contains more information than the original text. If there is some nlab policy on wiki-ed texts suggesting otherwise, please let me know.

- Discussion Type
- discussion topicdependent type formulation of internal diagrams
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 3
- Last comment by Mike Shulman
- Last Active May 26th 2012

- I've added a formulation of internal diagrams using dependent types.

- Discussion Type
- discussion topicdefinable set
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 25th 2012

Finally, definable set.

- Discussion Type
- discussion topiclocally bounded category
- Category Latest Changes
- Started by Emily Riehl
- Comments 7
- Last comment by FinnLawler
- Last Active May 25th 2012

I created locally bounded category with basic results from papers of Kelly and Lack. My motivation (unfortunately not reflected in the current stub) is to provide a reference for convergence conditions for the free monad construction.

On this topic, does anyone know whether there are reasonable conditions under which the dual “free comonad” construction would converge? I’m concerned by the result at locally presentable category (new to me; does anyone have a reference?) which says that the opposite of a locally presentable category is locally presentable only if the category is a poset.

- Discussion Type
- discussion topictheory
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 25th 2012

I have expanded theory adding more basics in classical syntactic approach. I added a new subsection

#### Set-theoretic models for a first-order theory in syntactic approach

The basic concept is of a structure for a first-order language $L$: a set $M$ together with an interpretation of $L$ in $M$. A theory is specified by a language and a set of sentences in $L$. An $L$-structure $M$ is a

**model**of $T$ if for every sentence $\phi$ in $T$, its interpretation in $M$, $\phi^M$ is true (“$\phi$ holds in $M$”). We say that $T$ is**consistent**or satisfiable (relative to the universe in which we do model theory) if there exist at least one model for $T$ (in our universe). Two theories, $T_1$, $T_2$ are said to be**equivalent**if they have the same models.Given a class $K$ of structures for $L$, there is a theory $Th(K)$ consisting of all sentences in $L$ which hold in every structure from $K$. Two structures $M$ and $N$ are

**elementary equivalent**(sometimes written by equality $M=N$, sometimes said “elementarily equivalent”) if $Th(M)=Th(N)$, i.e. if they satisfy the same sentences in $L$. Any set of sentences which is equivalent to $Th(K)$ is called**a set of axioms**of $K$. A theory is said to be**finitely axiomatizable**if there exist a finite set of axioms for $K$.A theory is said to be

**complete**if it is equivalent to $Th(M)$ for some structure $M$.

- Discussion Type
- discussion topicanalytic space
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by zskoda
- Last Active May 24th 2012

I have started an entry analytic space with material on Berkovich’s non-rigid analytic geometry.

I don’t really know this subject and have been adding material to the entry as I read about it and to the extent that I correctly understood it. Experts are most welcome to help out.

As indicated here, I am motivated by the following: Berkovich’s local contractibility result suggests that the $\infty$-topos of $\infty$-sheaves over the site of $p$-adic analytic spaces might be cohesive.

The idea would be that his result implies (if it does) that the site (category with coverage) of

*contractible*$p$-adic afine spaces is a dense subsite of that of all $p$-adic spaces. Since it should be an infinity-cohesive site that would imply the claim.But despite looking through Berkovich’s writings for a little bit today, I am still not sure if he just shows that the underlying topological space of a $p$-adic anayltic space is locally contractible, or if one may indeed deduce that they are locally contractible with respect to étale homotopy, as would be needed for the above conclusion.

- Discussion Type
- discussion topicGalois-Lascar group
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 23rd 2012

Stub for Lascar group, the analogue of Galois group for first order theories.

- Discussion Type
- discussion topicgeneralized vielbein
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 22nd 2012

created

*generalized vielbein*

- Discussion Type
- discussion topicformal scheme
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 5
- Last comment by Stephan A Spahn
- Last Active May 22nd 2012

I added a definition-section to formal scheme with the four equivalent definitions of a k-formal scheme from Demazure, lectures on p-divisible groups. There is some overlap with the section on Noetherian formal schemes now.

- Discussion Type
- discussion topicgenus / Witten genus
- Category Latest Changes
- Started by Urs
- Comments 48
- Last comment by Urs
- Last Active May 22nd 2012

created stubs for

This is not supposed to be satisfactory content. I just wanted these pages to exist right now, so that links to them work.

- Discussion Type
- discussion topicWhitehead tower
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 21st 2012

I treid to clean up Whitehead tower a bit:

I rewrote and expanded the Idea/Definition part.

Then I

*moved*David Roberts' material that was there to the appropriate section at the new Whitehead tower in an (infinity,1)-topos. (There I tried to add some introductory remarks to it but will try to further highlight David's results here in a moment).At Whitehead tower I left just a new section that says that there is a notion of Whitehead towers in more general contexts with a pointer to Whitehead tower in an (infinity,1)-topos

- Discussion Type
- discussion topicdouble cover
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 21st 2012

felt like creating

*double cover*

- Discussion Type
- discussion topicgeneralized tangent bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 21st 2012

felt like creating

*generalized tangent bundle*

- Discussion Type
- discussion topicactions
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by TobyBartels
- Last Active May 21st 2012

Uday has added :

Mac Lane, VII.4, only requires a monoidal category to define actions. – at action.

This takes up an old point that I made but never felt up to following up.

- Discussion Type
- discussion topiclocally cartesian closed category
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Mike Shulman
- Last Active May 21st 2012

at

*locally cartesian closed category*I have added a Properties-section*Equivalent characterizations*with details on how the slice-wise internal hom and the dependent product determine each other.This is intentionally written in, supposedly pedagogical, great detail, since I need it for certain discussion purposes. But looking back at it now, if you say it is

*too*much notational detail, I will understand that :-). But I think it’s still readable.

- Discussion Type
- discussion topicstack semantics for locally internal categories
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 2
- Last comment by zskoda
- Last Active May 20th 2012

- I've added a few examples to stack semantics illustrating how it can be used to talk about locally internal categories (in the sense of the appendix of Johnstone's Topos Theory).

- Discussion Type
- discussion topicBarratt-Eccles operad
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by zskoda
- Last Active May 18th 2012

stub for Barratt-Eccles operad

- Discussion Type
- discussion topiccategorical wreath product
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 18th 2012

categorical wreath product. Finally.

- Discussion Type
- discussion topicdivisible group
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 4
- Last comment by zskoda
- Last Active May 18th 2012

I added the characterization of a divisible abelian group as an injective object in the category of abelian groups to divisible group.

- Discussion Type
- discussion topicquasicompact
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by TobyBartels
- Last Active May 17th 2012

I changed quasicompact to quasicompact morphism though it is also about quasicompact schemes etc. as before and moved the query box here:

Mike: To accord with terminological conventions, this page should probably be either “quasicompact space” or “quasicompact object.”

Zoran Skoda: I do not know what are the conventions, but it was intentional to look both at quasicompact spaces and quasicompact morphisms (which are according to the dominant point of view in algebraic geometry, more important and basic notion); and aside also for q. objects. Personally I do not understand English-language preference for noun phrases. If one is to choose, quasicompact morphism is the choice.

*Toby*: By the «Each definition gets its own page.» convention, I'm not even sure that this shouldn't just redirect to compact space or compact object. My impression is that assuming that ’compact’ implies Hausdorff is either (like assuming that ’ring’ implies commutative) restricted to fields where it's a common assumption or to languages (I'm thinking mostly of Bourbaki in French here) other than English. On the other hand, if it's used that way by English-writing algebraic geometers, then I would seem to be wrong (since algebraic geometers often have non-Hausdorff spaces).Zoran Skoda: Convention that ’compact’ includes Hausdorff is very common also among people working predominantly on nice spaces, particularly differetial geometers, differential topologists, people studying metric spaces and so on. But for “paracompact” the situation is more tricky: in literature, even on general topology there are also competing definitions, which are all equivalent for Hausdorff spaces. All my life I bounce in such people; my own education does not assume Hausdorffness, unless it is said in the form “compactum”. Algebraic geometers always say quasi-compact, it has nothing to do with language; but as I say for algebraic geometers the basic notion is quasi-compact. The emphasis of this entry is on the terminology and morphisms (what should be expanded on: I still did not write the deifnitions of quasi-compact MORPHISM in various setups); so redirection won’t work I think. Plus although from my point of view saying quasicompact and compact is the same for spaces; one would never say compact for the scheme; scheme is said to be quasicompact if its underlying space is (quasi)compact.

There is an additional reason for that: one can consider a nonsingular variety over complexes which is quasicompact, and which itself is not compact in complex topology (under GAGA). But in the same considerations it is often useful to have some arguments in Zariski and some in complex topology; one of the reasons for word quasicompact is that sometimes we have the “same” example which we are used to think as of noncompact space but it is (quasi)compact in Zariski topology. When an algebraic geometer thinks of the difference between compact and quasicompact for complex varieties he has that in mind; in more general setups about Hausdorff vs nonHausdorff. In the same time, when talking about objects in derived categories of qcoh sheaves, even algebaric geometers use moreoften term compact than quasicompact; thus redirecting to compact object and saying this is for algebraic geometry won’t do for all the 3 notions in this entry (on the contrary side, nobody says compact morphism as far as I could confirm, but quasicompact morphism).*Toby*: Ah, so when you've got both Zariski and complex topologies around, you can easily distinguish the former by the prefix ’quasi’; that's cute. Anyway, perhaps we'll move this to quasicompact morphism if you write mostly about that, but I won't try to move anything for now.

- Discussion Type
- discussion topicuniformly hyperfinite algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active May 17th 2012

stub for

*uniformly hyperfinite algebra*

- Discussion Type
- discussion topicGamma spaces and theories
- Category Latest Changes
- Started by fpaugam
- Comments 9
- Last comment by fpaugam
- Last Active May 16th 2012

- I would like to understand what kind of theory Gamma is, in the sense of doctrines.

This is not included on the Gamma-space page, and i would like something about

that to be here, so this discussion is making a proposition in this sense.

I mean that Delta maclane may be seen as the algebraic theory of monoids (category

with finite products opposite to that of finitely generated free monoids), and its

models in sets are monoids, and in categories are monoidal categories (pseudo-functors).

For Gamma, it is not an algebraic theory, since n is not the product of n times 1, but

it seems to me something like a monoidal theory. I would tend to define Gamma of

Segal as a kind of theory of commutative monoids in monoidal categories, obtained

by adding to the operations in Delta (monoidal structure) additional symmetry data.

For example, if i take a monoidal functor from Gamma to sets, i get a commutative

monoid, whose underlying monoid is the model of Delta (algebraic theory), but

the theory Gamma seems monoidal, not algebraic in the sense of Lawvere.

These notions are important to better understand higher categorical generalizations

of monoidal and symmetric monoidal categories.

Am i correct here? May we add these theoretical/doctrinal considerations to the Gamma-spaces

page to clarify where Gamma is coming from, from a conceptual/theoretical point of view?

- Discussion Type
- discussion topicthe adjunction between type theories and categories
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active May 16th 2012

While the lab is down, I’ll collect some stuff here, also to discuss it.

So I am trying to identify in the literature a precise and coherent statement of the supposed adjunction / partial equivalence between “type theories” and “categories”.

In section 8.4.C of Practical Foundations is announced the following, which would be part of that statement:

- Every category with a rooted class of display maps is equivalent to a category of contexts of (and now I think it can read:) a dependent type theory.

Unfortunately the online version of the book breaks off right after this announcement, and I don’t have the paper version available at the moment.

Also, that section 8.4.C starts with the word “Conversely”. But where is the converse statement, actually?

- Discussion Type
- discussion topicfield net
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 14th 2012

I have created a stub

*field net*to go with*net of local observables*(for the moment mainly such as to record references)

- Discussion Type
- discussion topicDHR superselection theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 14th 2012

at

*DHR superselection theory*I have added the argument (here) for why every DHR representation indeed comes from a net-endomorphism, assuming Haag duality and that the net takes values in vN algebras.

- Discussion Type
- discussion topicquantum lattice system
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 14th 2012

started stub for

*quantum lattice system*, for the moment mainly as a reminder for me concerning the book by Bratteli now referenced there.

- Discussion Type
- discussion topicfull and faithful (infinity,1)-functor
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by TobyBartels
- Last Active May 14th 2012

- Discussion Type
- discussion topicRecursion
- Category Latest Changes
- Started by TobyBartels
- Comments 8
- Last comment by TobyBartels
- Last Active May 13th 2012

As reported elsewhere, Zhen Lin began recursion. I changed the section title “In classical mathematics” to “In general” since there didn’t seem to be anything inherently classical about it. But maybe I’m missing something.

- Discussion Type
- discussion topicpresentation of homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by TobyBartels
- Last Active May 13th 2012

I am working on prettifying the entry

*contractible type*and noticed that where in*Categorical semantics*it says “Let … with sufficient structure…” we really eventually need to point to an entry that discusses this sufficient structure in detail.In lack of a better idea, I named that entry

*presentation of homotopy type theory*. Feel free to make better suggestions.

- Discussion Type
- discussion topicinitial algebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Mike Shulman
- Last Active May 12th 2012

I have tidied up the entry

*initial algebra*and then made sure that it is cross-linked with*inductive type*(which it wasn’t!).We really need to rename this entry to

*initial algebra for an endofunctor*. But since I would have to fight the cache bug if I did it now, I decide not to be responsible for that at the moment.

- Discussion Type
- discussion topicfield with one element
- Category Latest Changes
- Started by zskoda
- Comments 12
- Last comment by zskoda
- Last Active May 11th 2012

More at field with one element, after creating person entry Christophe Soulé about the creator. By the way the Soulé has different encoding in n-Forum than in nlab so the link does not access the right page from here. See redirect Christophe Soule.

- Discussion Type
- discussion topicfiltered colimit
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by TobyBartels
- Last Active May 11th 2012

I have added various basic technical details to filtered colimit and flat functor.

- Discussion Type
- discussion topicseparated geometric morphism
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active May 9th 2012

created stub for

*separated geometric morphism*There is room to go through the Lab and interlink all the various entries on separated schemes, Hausdorff spaces etc. pp. and explain how these are all examples of a single notion. But I don’t have the energy for it right now.

- Discussion Type
- discussion topicJouanolou cover
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 7th 2012

New entry Jouanolou cover (prompted by its use in Van den Bergh’s version of a proof that every projective variety is a quiver Grassmanian, which JOhn posts about in cafe). Let me mention also the earlier entry Jean-Pierre Jouanolou.

- Discussion Type
- discussion topic(infinity,1)-vector bundle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 4th 2012

started (infinity,1)-vector bundle with a bit of discussion of the Ando-Blumberg-Gepner-Hopkins-Rezk theory of (discrete) $\infty$-ring module $\infty$-bundles.

- Discussion Type
- discussion topicexhaustive category
- Category Latest Changes
- Started by Mike Shulman
- Comments 8
- Last comment by Urs
- Last Active May 3rd 2012

I have created exhaustive category — not just the page, but the terminology. No one at MO seemed to know a name for this exactness property, so I made one up. The adjective “exhaustive” seems harmonious with “extensive” and “adhesive”, and expresses the idea that the subobjects in a transfinite union “exhaust” the colimit. But I would welcome other opinions and suggestions.

- Discussion Type
- discussion topicadhesive categories
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by Urs
- Last Active May 2nd 2012

Created adhesive category.

- Discussion Type
- discussion topicstrongly compact topological space
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 2nd 2012

of course there is also the notion going by the name

*strongly compact topological space*.

- Discussion Type
- discussion topiccurved dg-algebra
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by zskoda
- Last Active May 1st 2012

started curved dg-algebra

- Discussion Type
- discussion topicepipresheaf - ''minus construction''
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 1
- Last comment by Stephan A Spahn
- Last Active Apr 30th 2012

I added a definition to epipresheaf. I am wondering if there is a ”minus construction” turning a presheaf into an epipresheaf.

- Discussion Type
- discussion topicJames Wallbridge on (oo,1)-Tannakian theory
- Category Latest Changes
- Started by DavidRoberts
- Comments 8
- Last comment by Tim_Porter
- Last Active Apr 27th 2012

James Wallbridge put on the arXiv a paper derived from his thesis. I’ve linked to both from his page here. Urs, in particular, was interested in seeing a copy

- Discussion Type
- discussion topiccompact object in an (infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Apr 27th 2012

at compact object in an (infinity,1)-category I have added the definition and stated the examples: the $\kappa$-compact objects in $(\infty,1)Cat$/$\infty Grpd$ are the essentially $\kappa$-small $(\infty,1)$-categories/groupoids.

- Discussion Type
- discussion topicKan complexes as ∞-groupoids
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 14
- Last comment by Urs
- Last Active Apr 26th 2012

I would like to rearrange Kan complexes as ∞-groupoids to something like

general description

2-dimensional example

In particular I think the word oriental should occur more prominently in the beginning of this section.

- Discussion Type
- discussion topic[[line integral]]
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Apr 26th 2012

New page: line integral (also redirects from contour integral). Too damn long; somebody should edit this down.

- Discussion Type
- discussion topicinverse limit
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by TobyBartels
- Last Active Apr 26th 2012

added an illustrating diagram to

*inverse limit*, just so that one sees at one glance what the variance of the arrows is, since following through the “directed/codirected”-terminology and entries – if one really is in need of the $\mathbb{Z}_2$-orientation – can be a bit of a pain.

- Discussion Type
- discussion topicaction infinity-groupoid
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 1
- Last comment by Stephan A Spahn
- Last Active Apr 25th 2012

In need a definition of an action of a groupoid object $G$ in an ($\infty$,1)-category (actually in an ($\infty$,1)-topos) on an object $X$ - so I created one but I’m not yet sure if it coincides with the existing one if $X$ is pointed.

- Discussion Type
- discussion topicergodic theory
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Urs
- Last Active Apr 25th 2012

New stub ergodic theory wanted at measure theory.

- Discussion Type
- discussion topicteleparallel gravity
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by SridharRamesh
- Last Active Apr 22nd 2012

started

*teleparallel gravity*

- Discussion Type
- discussion topicWeitzenböck connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 21st 2012

stub for

*Weitzenböck connection*

- Discussion Type
- discussion topicComplexes of groups
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Urs
- Last Active Apr 19th 2012

I have started a new entry on complexes of groups, the higher dimensional version of graphs of groups (in the bass-Serre theory). These are related to orbifolds and topological stacks, but as yet there is just a stub. I have put some stuff in the Menagerie so will transfer more across in a short while (I hope!).

- Discussion Type
- discussion topicEilenberg subcomplex
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 19th 2012

started

*Eilenberg subcomplex*

- Discussion Type
- discussion topicmodel structure for dendroidal complete Segal spaces
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 18th 2012

Have been adding material to

*model structure for dendroidal complete Segal spaces*.

- Discussion Type
- discussion topicReedy model structure over the simplex category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 15th 2012

I added to Reedy model structure in the section Over the simplex category a bunch of basic useful lemmas and proofs. It works up to a proof of the Bousfield-Kan map.

- Discussion Type
- discussion topicderived geometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 15th 2012

for a seminar that we will be running I need a dedicated entry

So I created it.

I inserted a disclaimer on top that there are variants to what people understand under “derived geometry” and point the reader to the entry higher geometry for more details. I would be grateful if we could keep this entry titled this way and discuss variants elsewhere.

I would also be grateful if anyone who feels like making non-controversial edits (typos, references, etc. ) to for the moment do them not on this nLab page, but on this page here on my personal web:

Because currently the content of both pages is identical – except that the latter also has a seminar schedule which is omitted in the former – and until the entry has stabilized a bit more I would like to make edits just in

*one*place and update the other one by copy-and-paste.

- Discussion Type
- discussion topiclocal fibration
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Apr 14th 2012

quick note

*local fibration*

- Discussion Type
- discussion topicreduced simplicial set
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 14th 2012

created

*reduced simplicial set*, just for completeness

- Discussion Type
- discussion topicF-finite sets
- Category Latest Changes
- Started by TobyBartels
- Comments 19
- Last comment by Mike Shulman
- Last Active Apr 10th 2012

Although there is a standard meaning of ‘finite’ in constructive mathematics, it’s helpful to have a way to indicate that one really means this and is not just sloppily writing ‘finite’ in a situation where it is correct classically, without having to make a circumlocution like ‘finite (even in constructive mathematics)’. Based on Mike’s notation at finite set and drawing an analogy with ‘$K$-finite’, I’ve invented the term ‘$F$-finite’. (So now the circumlocution is simply ‘finite ($F$-finite)’ or ‘finite (F-finite)’, assuming that one wishes to relegate constructivism to parenthetical remarks.)

I’ve added this to finite set, added redirects, and used the new abbreviated circumlocution at dual vector space.

- Discussion Type
- discussion topicIndroduction to a simplicial model of homotopy type theory
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 3
- Last comment by Stephan A Spahn
- Last Active Apr 5th 2012

I created T. Streicher - a model of type theory in simplicial sets - a brief introduction to Voevodsky’ s homotopy type theory with a summary of that article and linked it from homotopy type theory. Maybe this article can serve as a base for some pedagogical nlab-entry providing some technical details concerning this simplicial model which are omitted in homotopy type theory.