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Category Theory

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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra || part of the +mathematics:matrix.org community45 Servers

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2 Dec 2019
@joel135:matrix.orgJoel Sjögren for some reason i associated monos with coproduct rather than product 19:45:32
@joel135:matrix.orgJoel Sjögren but of course, topos theory is about monos and pullbacks 19:46:50
@thosgood:matrix.orgTimmm, i think it maybe helps to remember that monomorphisms are more general versions of equalisers (which are limits, like products)19:46:51
@joel135:matrix.orgJoel Sjögren yes i agree 19:47:11
6 Dec 2019
@khinchin:matrix.orgKhinchin joined the room.18:04:11
@bkl:matrix.orgBohdan joined the room.22:47:36
7 Dec 2019
@bbbbrrrzzt:matrix.orgbbbbrrrzzt joined the room.05:10:12
9 Dec 2019
@joel135:matrix.orgJoel Sjögren Hmm, this seems like a Yoneda type of property. 12:56:21
@joel135:matrix.orgJoel Sjögren v(-,a)=\int_x(x a,v x) 12:57:16
@joel135:matrix.orgJoel Sjögren for v:\hat{A}\to E, x:A^\mathrm{op}\to E, a:A 12:59:03
@joel135:matrix.orgJoel Sjögren * for v:\hat{A}\to E, x:A^\mathrm{op}\to \mathrm{Set}, a:A12:59:49
@joel135:matrix.orgJoel Sjögren * for $v:\hat{A}\to E$, $x:A^\mathrm{op}\to \mathrm{Set}$, $a:A$13:00:06
14 Dec 2019
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17 Dec 2019
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21 Dec 2019
@jehaverlack:matrix.orgjehaverlack joined the room.18:49:45
@jehaverlack:matrix.orgjehaverlackIs anyone familiar with Jacob Lurie's work on Higher Topos Theory / Infinite Categories?18:50:58
@jehaverlack:matrix.orgjehaverlackI'm interested in a conceptual introduction, the best I've found is this article: https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/18:51:59
@bbbbrrrzzt:matrix.orgbbbbrrrzzt Yes and I've read that precise articled 21:18:51
@bbbbrrrzzt:matrix.orgbbbbrrrzztYou can download his work on his website21:19:05
@jehaverlack:matrix.orgjehaverlackThanks, I've done so.22:48:17
@jehaverlack:matrix.orgjehaverlackSomeone in another channel pointed me at: https://arxiv.org/abs/1907.0290422:49:22
23 Dec 2019
@test5864346:matrix.orgtest5864346 joined the room.12:51:17
@thosgood:matrix.orgTimif it’s his general infinity category stuff then you can read a bunch of stuff on his approach16:26:49
@thosgood:matrix.orgTim which is via quasicategories 16:26:56
@thosgood:matrix.orgTimi think stuff by emily riehl for example is way better written as a thing to learn from16:27:17
@thosgood:matrix.orgTimthere’s also a book by bergner which is meant to be v good16:28:20
@jehaverlack:matrix.orgjehaverlackThanks for the recomendations!20:23:07
@thosgood:matrix.orgTimno problem :) let us know if you have any other questions too!23:10:04
28 Dec 2019
@khinchin:matrix.orgKhinchin
In reply to @thosgood:matrix.org
there’s also a book by bergner which is meant to be v good
As you talk about Bergner book, I know that it is about homotopy theory. How do you feel about the book by Cisinski?
18:21:18
@thosgood:matrix.orgTim i’m not familiar with it, but i know that one of his books is apparently quite unrigorous 19:15:16

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