Category Theory

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a place to discuss category theory, both applied and theoretical, and any other related things | part of the +mathematics:matrix.org community3 Servers

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28 Dec 2019
19:15:40@thosgood:matrix.orgTimbut i have no personal experience with it
19:15:48@thosgood:matrix.orgTimand i could be misremembering
29 Dec 2019
23:55:13@warculture:matrix.orgwarculture joined the room.
30 Dec 2019
22:42:31@cbertram:matrix.orgChristian Bertram joined the room.
22:47:25@cbertram:matrix.orgChristian BertramHi, I have a very simple question, I hope that's okay. 🙂 Is Cat locally small? I think it is, as I guess small categories can be represented as sets,(?) and Sets is locally small. Not sure, though
22:54:53@thosgood:matrix.orgTimis Cat the category of small categories?
22:55:02@cbertram:matrix.orgChristian BertramYes
22:56:26@thosgood:matrix.orgTim huh, i guess so...
23:02:58@cbertram:matrix.orgChristian BertramI "guess", because my book makes it sound to me as if Cat is not locally small. "Pos, Top and Group are locally small (is Cat?)"
23:04:47@cbertram:matrix.orgChristian BertramI am sorry if this sounds like a stupid homework question. It is not, I am not taking a course, just trying to learn some mathematics
23:06:11@thosgood:matrix.orgTimno, it’s a good question!
23:06:33@thosgood:matrix.orgTimprobably obvious to a category theorist, but i’m always very nervous about such details...
23:11:28@cbertram:matrix.orgChristian BertramAh okay, thanks! If you think it's a detail I will not worry more about it, I will probably find out later if it turns out not to be true
23:20:17@thosgood:matrix.orgTimtwo twitter responses
23:20:43@thosgood:matrix.orgTimvery different but probably both good answers!
23:28:06@cbertram:matrix.orgChristian BertramHehe thank you! Ah I see, concrete category was what I was trying to get at with "can be represtented as sets", so my thinking was about right. But yep, probably both good answers :)
23:45:22@thosgood:matrix.orgTimso you just need to check that the class of functors between any two locally small sets is a set
23:46:22@thosgood:matrix.orgTimand you use the fact that your categories are locally small (this is key!)
31 Dec 2019
00:16:08@cbertram:matrix.orgChristian BertramAre you thinking of proving that the category of locally small categories is itself locally small? I was only thinking about proving that the category of small categories is locally small, which must come from the fact that the class of functors between two small categories is a subset of X^Y
00:16:51@cbertram:matrix.orgChristian Bertramoops, pressed enter
00:17:02@thosgood:matrix.orgTimoh woops, sorry, that’s what i meant
00:17:14@thosgood:matrix.orgTim you’re right
00:18:10@cbertram:matrix.orgChristian BertramOkay, no problem, thanks a lot!
2 Jan 2020
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3 Jan 2020
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6 Jan 2020
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8 Jan 2020
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19 Jan 2020
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20 Jan 2020
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