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Stream: learning: questions

Topic: functoriality of cod fibration

view this post on Zulip Christian Williams (Apr 01 2021 at 03:19):

The construction which sends a category with finite limits CC to its codomain fibration codC:[I,C]→Ccod_C:[I,C]\to C defines a 2-functor cod:Lex→Fibcod:Lex\to Fib. Does someone know a good reference for this? Currently I'm just writing it up myself. Thanks.

view this post on Zulip Christian Williams (Apr 01 2021 at 03:35):

There should be a whole family of similar theorems, describing the functoriality of constructing different kinds of fibrations for different classes of structured categories. It would be useful to have a complete reference for these.

view this post on Zulip Jacques Carette (Apr 01 2021 at 14:53):

I wonder if it's buried somewhere in Bart Jacobs' "Categorical Logic and Type Theory"?

view this post on Zulip Christian Williams (Apr 01 2021 at 15:08):

That's what I would guess, but I haven't found it yet.

view this post on Zulip John Baez (Apr 01 2021 at 15:13):

It'd be good to ask in a short post on the n-Cafe, as well as doing a serious search online - while simultaneously charging ahead and proving a family of theorems of this type.

view this post on Zulip Peter Arndt (Apr 01 2021 at 21:31):

Here's a family of cods: cod.jpeg