Timeline for Results in “generalised smooth spaces” that did not hold in the case of smooth manifolds
Current License: CC BY-SA 4.0
13 events
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Jun 26, 2020 at 1:19 | comment | added | Praphulla Koushik | For anyone else looking for more references, they can see “17.7 Internal Hom” of Masaki Kashiwara and Pierre Schapira’s book titled “Categories and Sheaves”. | |
Jun 24, 2020 at 3:22 | comment | added | Praphulla Koushik | Sorry. I was looking at table of contents and was lost in 8+ table of contents. Thanks for the reference. I feel like I might enjoy reading parts of this book. | |
Jun 24, 2020 at 1:49 | comment | added | Dmitri Pavlov | @PraphullaKoushik: Sections 1.57–1.65. | |
Jun 24, 2020 at 0:54 | comment | added | Praphulla Koushik | That book looks interesting (too lengthy though:)) but I do not see where does they talk about the internal hom description :O | |
Jun 23, 2020 at 23:54 | history | bounty ended | Praphulla Koushik | ||
Jun 23, 2020 at 23:23 | comment | added | Dmitri Pavlov | @PraphullaKoushik: Patrick Iglesias-Zemmour, Diffeology. It's all about diffeological spaces (and sheaves of sets on manifolds). | |
Jun 23, 2020 at 16:07 | comment | added | Praphulla Koushik | Yes, I saw that explanation only recently.. I am still trying to look at the motivation behind such description of the inner-hom/internal-hom $\text{Hom}(M,N)$.. I am reading MacLane and Moedijk's Sheaves in Geometry and Logic (3.6 first properties of categories of sheaves).. Do you have any suggestion on any other book that I should be looking at? | |
Jun 23, 2020 at 14:51 | comment | added | Dmitri Pavlov | @PraphullaKoushik: Just to be clear, Hom(M,N) denotes the sheaf whose S-points are smooth maps S⨯M→N. In particular, the points of Hom(M,N) are precisely the smooth maps M→N. Hom is right adjoint to the (categorical cartesian) product of sheaves of sets, defined objectwise: (F⨯G)(S)=F(S)⨯G(S). | |
Jun 22, 2020 at 21:04 | vote | accept | Praphulla Koushik | ||
Jun 22, 2020 at 21:05 | |||||
Jun 21, 2020 at 4:42 | comment | added | Praphulla Koushik | I have some other questions, but I should at least read the Freed-Hopkins paper first :) Thanks for this answer (really).. :) :) | |
Jun 21, 2020 at 4:39 | comment | added | Praphulla Koushik | This is interesting.. For manifolds $M.N$, as the mapping space $\text{Map}(M,N)$ is not expected to have a nice smooth structure, you would like to see $M$ and $N$ as objects of the category $Sh(\text{Man})$ and taking then take the internal-hom object of $M,N$ (I do not know why it exists, I will check details; I guess here "the tensor" is tensor product of sheaves).. | |
Jun 20, 2020 at 22:09 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 810 characters in body
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Jun 20, 2020 at 21:57 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |