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added pointer to:
Added a reference
On occasion of Alexander Schenkel’s most recent talk (here) I am finally splitting off an entry homotopical algebraic quantum field theory from AQFT.
This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:
In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.
Here are examples:
A quiver is just a directed graph (pseudograph, to be explicit). But one says quiver instead of directed graph when one is interested in studying quiver representations: functors from the free category on that graph to the category of finite-dimensional vector spaces.
A presheaf is just a contravariant functor. But one says presheaf instead of contravariant functor when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.
(…)
added the following pointers on non-deterministic automata as 1-dimensional defect TQFTs:
Paul Gustafson, Mee Seong Im, Remy Kaldawy, Mikhail Khovanov, Zachary Lihn, Automata and one-dimensional TQFTs with defects [arXiv:2301.00700]
Mee Seong Im, Correspondence between automata and one-dimensional Boolean topological theories and TQFTs, talk at QFT and Cobordism, CQTS (Mar 2023) [web]
In the course of doing so I tried to fix some oddities in this neglected entry. But I don’t have time to do it justice.
started to (re)structure the entry higher category theory roughly along the lines of the new structure at category theory. But for the moment many sections just contain link lists.
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
stub for quantum computation
added this pointer on the universal Vassiliev invariant of the unknot:
Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).
On (topological) inertia stacks
I have added to BPS state and to wall crossing pointers to two introductory lecture notes
I have created stratified space in order to collect some references
I have tried to start a table at maximal compact subgroup listing Lie groups and their max compact subgroups. But once again the table does not want to typeset properly.
Have to run now, will try to fiddle with this later.
have created enriched bicategory in order to help Alex find the appropriate page for his notes.
Added Peter Haine article and his claim to have proved the stratified homotopy hypothesis.
Created poset-stratified space. I wasn’t sure what to call this, since the references generally just call it a “stratified space”, but our page stratified space is about all notions of stratified space rather than just one of them. Suggestions are welcome.
(Am now listening to John Francis talk about these things at the Mid-Atlantic Topology Conference.)
New entry string topology, short sentence and several complete references, with links.
I have edited a bit at Fredholm operator. Also started a stubby Fredholm module in the process. But it remains very much unfinished. Have to interrupt now for a bit.
Wrote a section on the associated monad at operad, in terms of the framework introduced under the section titled Preparation.