5 Sep 2019 |

14:48:13 | Tim | sure |

14:48:19 | Tim | * sure |

14:49:17 | Joel Sjögren | it 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 | Joel Sjögren | so then you don't want j(xy)=j(y)j(x) for all x, y |

14:50:02 | Tim | ok, i think i see |

14:50:44 | Tim | is 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 | Tim | so, more generally, have a functor F:C->D with F contravariant on objects c:T and covariant on objects c:S |

14:51:40 | Tim | some sort of fibred construction |

14:52:08 | Tim | or maybe embed the two subcategories (corresponding to each type) into C, and work with two functors separately |

14:53:12 | Joel Sjögren | when 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 | Tim | yes, this |

14:53:43 | Tim | i'm not fully certain of what i'm trying to say, at least, not formally |

14:53:49 | Tim | just have a vague idea |

14:56:59 | Joel Sjögren | do we have (x->y) => (y*->x*)? |

14:57:28 | Tim | what is * here? |

14:57:35 | Tim | oh the dual |

14:57:36 | Joel Sjögren | dual |

14:58:35 | Tim | we should do, right? pretty sure you have this for pregroups anyway, but not certain here... |

14:59:34 | Joel 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 | Joel Sjögren | i need to make that code-style |

15:00:13 | Joel 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 | Tim | (or you can disable markdown for an individual message with the toggle button) |

15:00:33 | Tim | (or use https://pigeon.digital 😉) |

15:01:59 | Khinchin | 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 | Tim | just like latex: use enclose maths in $ signs (e.g. $x^2$) |

15:02:35 | Joel Sjögren | $\pi$ |

15:02:43 | Joel Sjögren | didn't work |

15:02:56 | Tim | are you on pigeon.digital? |

15:03:06 | Joel Sjögren | yes |

15:04:00 | Tim | ok, there's #pigeon.digital:matrix.org to discuss that then, to keep this room on topic 🙂 can help ya there |