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Applied Category Theory

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5 Dec 2019
18:20:05@telegram_771517137:t2bot.ioTobias Heindel (Telegram)
In reply to Jules Hedges
This is a usual thing. Remember that university administrators serve themselves, not researchers
Thanks for helping the good cause :)
18:25:49@telegram_503372818:t2bot.ioGNU/Brett G.
In reply to Jules Hedges
This is a usual thing. Remember that university administrators serve themselves, not researchers
Truth
20:26:24@telegram_637936590:t2bot.ioFrancisco
In reply to Tobias Heindel
Thanks for helping the good cause :)
Ha, nice! 😄
6 Dec 2019
07:02:07@telegram_1025279760:t2bot.ioAbdul set a profile picture.
12:03:40@telegram_926804993:t2bot.ioAndrea Censi
In reply to davidad
I thought about dinatural and extranatural, but I'm not sure. I think those fancier notions are only needed when a transform depends on *one* variable both co- and contra-variantly. That would be the case if, for example, you only wanted to map endomorphisms f : X→X over Sequences. But in your case X and Y are separate variables, and each is depended upon with only one variance, and so I think (though not very confidently) that it's an ordinary natural transformation.
On the left hand side we have both X->Y and Sequences[X]. X here appears both contravariant and covariant.
16:27:59@telegram_795415214:t2bot.iodavidad
In reply to Andrea Censi
On the left hand side we have both X->Y and Sequences[X]. X here appears both contravariant and covariant.
The transform is from the functor Hom(X,Y) to the functor Hom(Sequence(X),Sequence(Y)): X is contravariant in both occurrences (and Y is covariant)
22:48:38@telegram_59756535:t2bot.io joined the room.
7 Dec 2019
11:47:05@telegram_921949942:t2bot.ioJules Hedges Pre-announcement for the 2020 ACT Adjoint School: https://www.appliedcategorytheory.org/adjoint-school-act-2020/
11:47:20@telegram_921949942:t2bot.ioJules HedgesApplications will open soon, and will probably be due before the end of the year
11:47:42@telegram_921949942:t2bot.ioJules HedgesThe tutors are Valeria de Paiva, Mike Shulman, Mike Johnson and a 4th to be confirmed
11:47:54@telegram_921949942:t2bot.ioJules HedgesThe in-person part of the school will be at MIT in July
12:29:28@telegram_49574451:t2bot.ioDanieleNice
12:30:11@telegram_123618405:t2bot.ioWaifod
In reply to Jules Hedges
The in-person part of the school will be at MIT in July
Damn, that might be a problem.
12:31:50@telegram_921949942:t2bot.ioJules HedgesWhy, because of politics?
12:32:30@telegram_123618405:t2bot.ioWaifodNo, I will be defending my thesis in July.
12:34:37@telegram_921949942:t2bot.ioJules HedgesAh
12:36:35@telegram_921949942:t2bot.ioJules HedgesThere's not really anywhere good in the world to hold an international event, but the USA is still one of the worst in terms of who is able to travel there
14:28:52@telegram_141996935:t2bot.ioTx RxYesss
14:29:37@telegram_141996935:t2bot.ioTx RxMy friend has submitted his papers for visa 2 years ago and is still waiting
8 Dec 2019
07:06:34@telegram_771517137:t2bot.ioTobias Heindel (Telegram)
In reply to Jules Hedges
There's not really anywhere good in the world to hold an international event, but the USA is still one of the worst in terms of who is able to travel there
Barbados is great !
19:55:26@telegram_893650860:t2bot.io☕️ Lamp changed their profile picture.
9 Dec 2019
14:45:22@telegram_960270877:t2bot.ioEigil Rischel joined the room.
16:57:30@telegram_503372818:t2bot.ioGNU/Brett G. changed their profile picture.
10 Dec 2019
00:05:47@telegram_272098718:t2bot.ioEduardo OchsHey, anyone here knows a good formal proof that the "obvious" way of constructing explicitly the subobject classifier of a topos of the form Set^D, where D is a finite poset, works?
08:03:49@telegram_503372818:t2bot.ioGNU/Brett G. changed their profile picture.
11 Dec 2019
18:58:14@telegram_926804993:t2bot.ioAndrea Censi I found many answers regarding my question about the relation between parametric polimorphism and natural transformations in the paper "Theorems for Free" by Wadler. https://ecee.colorado.edu/ecen5533/fall11/reading/free.pdf
12 Dec 2019
14:51:41@telegram_897557541:t2bot.ioPhilip Zucker For people in the boston area are interested, I'm giving a small informal talk on relation algebra at the Categorical Databases meetup tonight. https://www.meetup.com/Categorical-Databases/events/266967988/
15:09:36@telegram_233142395:t2bot.ioApe ManI have a reference question about categories enriched in presheaf categories. Let A be some monoidal cat. Then PSh(A) has a monoidal structure given by Day convolution. I'm using PSh(A)-enriched categories for a project and I wonder what other applications these have. So I would be extremely grateful if someone can point out to a paper where these categories have been studied either in general or for some concrete choice of A. One way in which such categories arise is by a generalized Kleisli category construction: suppose I have an action F : A^op -> End(C) of the monoidal category A^op on C (by action I mean a lax monoidal functor, some people call this and actegory), then I get a PSh(A)-enrichment of C since a |-> hom(x, F(a,y)) gives me a presheaf (one has to check some compatibilities)
15:10:53@telegram_233142395:t2bot.ioApe ManI am also very interested in a reference for this Kleisli category construction, it's very natural so I would be very surprised if it hasn't been considered before
16:49:59@telegram_673570767:t2bot.ioDhruva changed their profile picture.

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