Category Theory

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5 Sep 2019
14:48:19@thosgood:matrix.orgTim * sure
14:49:17@joel135:matrix.orgJoel Sjögrenit seems to work in this case but if more reductions are defined maybe you want j(xy)=j(x)j(y) for those
14:49:41@joel135:matrix.orgJoel Sjögrenso then you don't want j(xy)=j(y)j(x) for all x, y
14:50:02@thosgood:matrix.orgTimok, i think i see
14:50:44@thosgood:matrix.orgTimis there not some construction that lets us make the variance of the functor depend on e.g. the type of the variable?
14:51:24@thosgood:matrix.orgTimso, more generally, have a functor F:C->D with F contravariant on objects c:T and covariant on objects c:S
14:51:40@thosgood:matrix.orgTimsome sort of fibred construction
14:52:08@thosgood:matrix.orgTimor maybe embed the two subcategories (corresponding to each type) into C, and work with two functors separately
14:53:12@joel135:matrix.orgJoel Sjögrenwhen you say variance, i take it that you mean that a monoidal category is a "2-category" (not sure about the terminology) with only one object. is this what you mean?
14:53:27@thosgood:matrix.orgTimyes, this
14:53:43@thosgood:matrix.orgTimi'm not fully certain of what i'm trying to say, at least, not formally
14:53:49@thosgood:matrix.orgTimjust have a vague idea
14:56:59@joel135:matrix.orgJoel Sjögrendo we have (x->y) => (y*->x*)?
14:57:28@thosgood:matrix.orgTimwhat is * here?
14:57:35@thosgood:matrix.orgTimoh the dual
14:57:36@joel135:matrix.orgJoel Sjögrendual
14:58:35@thosgood:matrix.orgTimwe should do, right? pretty sure you have this for pregroups anyway, but not certain here...
14:59:34@joel135:matrix.orgJoel Sjögren i think so. i'm trying to work out the variance of *. is it in some formal sense more true that (xy)* = y*x* than (xy)* = x*y*?
14:59:55@joel135:matrix.orgJoel Sjögreni need to make that code-style
15:00:13@joel135:matrix.orgJoel Sjögren * i think so. i'm trying to work out the variance of *. is it in some formal sense more true that (xy)* = y*x* than (xy)* = x*y*?
15:00:16@thosgood:matrix.orgTim(or you can disable markdown for an individual message with the toggle button)
15:00:33@thosgood:matrix.orgTim(or use https://pigeon.digital 😉)
In reply to @thosgood:matrix.org
(or use https://pigeon.digital 😉)
I am using it but I still don't know how to type maths exprression
15:02:23@thosgood:matrix.orgTimjust like latex: use enclose maths in $ signs (e.g. $x^2$)
15:02:35@joel135:matrix.orgJoel Sjögren$\pi$
15:02:43@joel135:matrix.orgJoel Sjögrendidn't work
15:02:56@thosgood:matrix.orgTimare you on pigeon.digital?
15:03:06@joel135:matrix.orgJoel Sjögrenyes
15:04:00@thosgood:matrix.orgTim ok, there's #pigeon.digital:matrix.org to discuss that then, to keep this room on topic 🙂 can help ya there

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