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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.
(…)
brief category:people-entry for hyperlinking references at tensor network and at holographic entanglement entropy
created a stub for holographic entanglement entropy in reaction to this MO question.
brief category:people-entry for hyperlinking references at tensor network
brief category:people-entry for hyperlinking references at computational topology
a stub for the moment just so as to give a home to
and to cross-link with p-adic AdS/CFT correspondence and tensor network states.
I edited lambda-ring, added a definition from the thesis of John R. Hopkins. Later on I will add the definitions of Hazewinkel, too. This entry has a long (and very instructive) idea-section. Maybe I find time to fill in some more details to these ideas.
stub for cosmic inflation (for the moment just to record some references)
added pointer to today’s
at books about string theory I have added some paragraphs with descriptions of books in the first section (“Mathematically inclined monographs about string theory”)
I see that Ben Webster was so kind to start knot invariant.
That nicely supplies linkes for Bruce's recent Chern-Simons theory
brief category:people-entry for hyperlinking references at cohomotopy
added pointer to:
Strangely, we don’t seem to have an nForum discussion for probability theory.
I added a reference there to
It replaces the category of measurable spaces, which isn’t cartesian closed, with the category of quasi-Borel spaces, which is. As they point out in section IX, what they’re doing is working with concrete sheaves on an established category of spaces, rather like the move to diffeological spaces.
[Given the interest in topology around these parts at the moment, we hear of ’C-spaces’ as generalized topological spaces arising from a similar sheaf construction in C. Xu and M. Escardo, “A constructive model of uniform continuity,” in Proc. TLCA, 2013.]
on the occasion of adding one more recent reference (Wells 18) I gave the paragraphs criticizing the concept their own subsection Problems with the concept.
And then I took the liberty to add what I think is the key problem, which is however generally overlooked in these discussions, away from the small community of mathematical field theorists: Dependence on the renormalization scheme
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).
brief category:people-entry for hyperlinking references at AdS/CFT in condensed matter physics