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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
have added a tad more to the Properties-section at Riemann zeta function.
have created a “floating TOC” notions of subcategory and have included it in the relevant entries
Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “E10” from the top and added one for “E10” at the bottom of the page.)
A stub for M-theory. What’s supposed to be so mysterious about it? Is it that people don’t even know what form it would take?
the link to the picture in the entry Charles Wells is broken. Does anyone know how to fix it or have an alternative picture?
Added this pointer:
An early discussion of automata via string diagrams in the Cartesian monoidal category of finite sets:
- Günter Hotz, Eine Algebraisierung des Syntheseproblems von Schaltkreisen, EIK, Bd. 1, (185-205), Bd, 2, (209-231) 1965 (part I, part II, compressed and merged pdf)
incuding that new compressed and merged pdf which I produced, as a service to the community.
In looking for texts that would address the question “What is computation?” and arrive at an answer vaguely akin to path lifting/transport, I found (and have now added pointer to) this text:
which gets pretty close, in particular in and around their Figure 1.
In locally cartesian closed category, I wrote out an explicit proof that pullback functors between slices preserve exponentials (so that Frobenius reciprocity is satisfied).
I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.
A stub recording a reference:
In a double category with companions, a retrocell is …
In the double category of spans, a retrocell boils down to a morphism of spans, where the source span is the pullback of the original source span along the corresponding horizontal arrow. (Paré, §5.)
Expanded dinatural transformation a little with examples and references.
added pointer to:
Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor
Todo: add more proofs of this result.
For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:
An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out
How can I fix this?
I added to initial object the theorem characterizing initial objects in terms of cones over the identity functor.
I am giving this bare list of references its own entry, so that it may be !include-ed into related entries (such as topological quantum computation, anyon and Chern-Simons theory but maybe also elsewhere) for ease of updating and synchronizing
added to polynomial functor the evident but previously missing remark why it is called a “polynomial”, here.
the entry braid group said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).
Stub Makkai duality, just recording the most basic references so far; linked from Stone duality.
added pointer to:
am too tired to do it now, but on occasion of an MO discussion:
remind me to insert at smooth manifold the statement and proof that smooth manifolds are equivalently the locally representable sheaves on CartSp (more precisely: the -schemes).
created supergravity
so far just an "Idea" section and a link to D'Auria-Fre formulation of supergravity (which i am busy working on)
I worked on synthetic differential geometry:
I rearranged slightly and then expanded the "Idea" section, trying to give a more comprehensive discussion and more links to related entries. Also added more (and briefly commented) references. Much more about references can probably be said, I have only a vague idea of the "prehistory" of the subject, before it became enshrined in the textbooks by Kock, Lavendhomme and Moerdijk-Reyes.
Also, does anyone have an electronic copy of that famous 1967 lecture by Lawvere on "categorical dynamics"? It would be nice to have an entry on that, as it seems to be a most visionary and influential text. If I understand right it gave birth to topos theory, to synthetic differential geometry and all that just as a spin-off of a more ambitious program to formalize physics. If I am not mistaken, we are currently at a point where finally also that last bit is finding a full implmenetation as a research program.
brief category:people-entry for hyperlinking references at symmetric function and Schur polynomial
changed higher algebra - contents to algebra - contents in context sidebar
Anonymouse
I came to think that the pattern of interrelations of notions in the context of locally presentable categories deserves to be drawn out explicitly. So I started:
Currently it contains the following table, to be further fine-tuned. Comments are welcome.
| | | inclusion of left exaxt localizations | generated under colimits from small objects | | localization of free cocompletion | | generated under filtered colimits from small objects | |–|–|–|–|–|—-|–|–| | (0,1)-category theory | (0,1)-toposes | | algebraic lattices | Porst’s theorem | subobject lattices in accessible reflective subcategories of presheaf categories | | | | category theory | toposes | | locally presentable categories | Adámek-Rosický’s theorem | accessible reflective subcategories of presheaf categories | | accessible categories | | model category theory | model toposes | | combinatorial model categories | Dugger’s theorem | left Bousfield localization of global model structures on simplicial presheaves | | | | (∞,1)-topos theory | (∞,1)-toposes | | locally presentable (∞,1)-categories | <br/> Simpson’s theorem | accessible reflective sub-(∞,1)-categories of (∞,1)-presheaf (∞,1)-categories | |accessible (∞,1)-categories |
have cleared this entry (formerly “semi-locally simply connected topological space”), since its content has beenmerged into semi-locally simply-connected topological space, following discussion there
added pointer to:
added pointer to
on formal proof and proof assistants in undergaduate mathematics courses
will add this also to formal proof and proof assistant
Stub Frobenius reciprocity.
created website-link page Denis-Charles Cisinski
At enriched category it uses to say that
A Top-enriched category is a topological category.
But then at topological category, which redirects to topological concrete category it says that it
does not mean Top-enriched category.
Of course for many people it does. But to get the Lab entries straight, and to go along with the entry simplicially enriched category, I started an entry
just for completeness (and since I need the material elsewhere).
