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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicnegative thinking
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 19th 2009

added to negative thinking an explicit list of related entries and the floating higher cat theory toc

I think this is important enough to show the reader as much of the grand picture as possible

- Discussion Type
- discussion topicNew article: TAC
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Urs
- Last Active Nov 19th 2009

I figured that we could stand to have an article on

*TAC*, so I started one.

- Discussion Type
- discussion topicGelfand-Neumark
- Category Latest Changes
- Started by David_Corfield
- Comments 14
- Last comment by zskoda
- Last Active Nov 19th 2009

- I thought I'd add something about the Gelfand-Neumark theorem

The category of commutative von Neumann algebras is contravariantly equivalent to the category of localizable measurable spaces.

to measurable space, but see we don't have anything on localizability.

I also mentioned the theorem at von Neumann algebra. But what should one then say that a general von Neumann algebra is a noncommutative localizable measurable space? Normally one says noncommutative measure space.

- Discussion Type
- discussion topicRequest for references at commutative algebraic theory
- Category Latest Changes
- Started by Andrew Stacey
- Comments 4
- Last comment by Andrew Stacey
- Last Active Nov 18th 2009

The stuff at commutative algebraic theory is very interesting and I'd like to know some references! *looks at Todd, Toby, and Gavin*

- Discussion Type
- discussion topicDanger Todd Trimble!
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Todd_Trimble
- Last Active Nov 18th 2009

I may have overlapped an edit with you at initial algebra. ( It's no longer locked, but you didn't change it again, so maybe it timed out.)

- Discussion Type
- discussion topicmodel structure on simplicial presheaves and related
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Mike Shulman
- Last Active Nov 18th 2009

Over on MO Denis-Charles Cisinki kindly replied to some issues that I am recently working on here. See this.

- Discussion Type
- discussion topicCograph
- Category Latest Changes
- Started by Eric
- Comments 45
- Last comment by Eric
- Last Active Nov 17th 2009

It's not technically part of the main nLab (yet), but I asked a question at

- Discussion Type
- discussion topicdouble nerve
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 17th 2009

created stub entry for double nerve in reply to this MO question.

- Discussion Type
- discussion topicmodel structure on homotopical presheaves
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2009

started model structure on homotopical presheaves, where I collect the information that Denis-Charles Cisinski kindly provided here

I created a section "higher oo-stacks" at infinity-stack with a sentence about and a link to that.

- Discussion Type
- discussion topicsimplicial manifold
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 17th 2009

created stub for simplicial manifold

- Discussion Type
- discussion topicn-symplectic manifold
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 17th 2009

created n-symplectic manifold

- Discussion Type
- discussion topicionads
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Nov 17th 2009

- Couple of points (pun not intended) at ionad. Also remark about categorified subobject classifiers

David Roberts

- Discussion Type
- discussion topicRearranged higher category theory contents
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Nov 17th 2009

I rearranged higher category theory - contents. It seemed wrong to have everything as a special case of -categories/-categories except for -categories/-categories. But it seemed right to list the latter up front, as the all-subsuming concept. So I basically reversed the order. (I also added a few entries.)

- Discussion Type
- discussion topicLambek's theorem; natural numbers
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Nov 16th 2009

- Added to initial algebra the proof of Lambek's theorem, that the algebra structure of an initial algebra is an isomorphism. Also added to natural numbers object Freyd's finite colimit characterization in a topos, with a partial proof of same.

- Discussion Type
- discussion topicThe remains of JA
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Mike Shulman
- Last Active Nov 16th 2009

We now have several new (or not so new) logic stubs: boolean domain, boolean function, boolean-valued function, higher-order logic, Peirce's law, propositional logic, ternary relation, type, Charles Sanders Peirce.

- Discussion Type
- discussion topicLevi-Civita connection
- Category Latest Changes
- Started by amathew
- Comments 2
- Last comment by Urs
- Last Active Nov 16th 2009

I created [[Levi-Civita connection]].

- Discussion Type
- discussion topicdiagrammatic order
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Mike Shulman
- Last Active Nov 16th 2009

Created diagrammatic order. I attempted to strike a neutral tone in describing the dispute, but if you think I failed, please help.

- Discussion Type
- discussion topicGeneralised smooth algebras
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Nov 13th 2009

I fixed some formatting and put up some boxes at generalized smooth algebra.

- Discussion Type
- discussion topicDold fibration
- Category Latest Changes
- Started by Guest
- Comments 9
- Last comment by Urs
- Last Active Nov 13th 2009

- Created Dold fibration

- Discussion Type
- discussion topicsuspension object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 13th 2009

quick stub for suspension object

- Discussion Type
- discussion topicfibration of bigroupoids
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Nov 13th 2009

- created fibration of bigroupoids - will gather soon there some relevant background and try to define what I feel is a topologically inspired version, springing from the brief discussion at Grothendieck fibration.

David Roberts

- Discussion Type
- discussion topicKlein-2-geometry links
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by David_Corfield
- Last Active Nov 12th 2009

- I've notices that the links at Klein 2-geometry to the earlier parts are broken (something to do with the pages at Geocities). I recall hearing that someone made some more permanent copies. Is this true and if so, where are they?

I said some embarrassingly naive things there, but one must preserve what progress was made.

-David Roberts

- Discussion Type
- discussion topicE-k-operad
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Mike Shulman
- Last Active Nov 12th 2009

created stub for E-k-operad

- Discussion Type
- discussion topiccochains on simplicial sets
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Eric
- Last Active Nov 11th 2009

created cochains on simplicial sets

I reference there a very useful but unpublished note by Peter May that he sent me by email after he got over his astonishment that I didn't know that the Eilenberg-Zilber E_oo operad acts on cochains on a simplicial set.

It would be great if I were allowed to upload this note to the nLab and link it at that entry. I'll see if I ask by email, but maybe Mike can mention it over lunch? I feel like Peter May feels already pestered enough by my ignorance.

- Discussion Type
- discussion topiccategorification
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 11th 2009

I expanded categorification a little.

I had intended to point to it from a MathOverflow question, but now I feel the entry is still too underdeveloped. Hopefully we'll eventually find the time and energy to enter the big examples that drive the interest in categorification.

- Discussion Type
- discussion topicEilenberg-Zilber operad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 11th 2009

created Eilenberg-Zilber operad

- Discussion Type
- discussion topicdirectory of personal webs
- Category Latest Changes
- Started by Andrew Stacey
- Comments 6
- Last comment by Eric
- Last Active Nov 11th 2009

- Discussion Type
- discussion topicbraided monoidal 2-categories
- Category Latest Changes
- Started by bwebster
- Comments 2
- Last comment by Urs
- Last Active Nov 10th 2009

I started a page on braided monoidal 2-category. Not that I have anything interesting to say on the subject, but I would like to know how to get them as module 2-categories over a monoidal category.

- Discussion Type
- discussion topicthin homotopy
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by Urs
- Last Active Nov 10th 2009

created [[thin homotopy]] to service [[bicategory]], at which I added the necessary qualifier ‘Hausdorff’ to the existence of the quotient of Pi_2 by thin homotopies. There is only a passing mention of the smooth version as I only needed the topological case.

-David Roberts

- Discussion Type
- discussion topicanafunctors between fibres of a Grothendieck fibration
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Nov 9th 2009

- At cartesian morphism a query/request for an anafunctor treatment of what is essentially the pseudofunctor associated to a fibration

David Roberts