Timeline for Why pullback only defined up-to-isomorphism but nevertheless presented as functor?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2012 at 20:41 | comment | added | Mike Shulman | @Ronnie: It's true that every fibration admits a canonical "ana-cleavage". Is that what you were asking? | |
| Dec 12, 2012 at 23:39 | comment | added | David Roberts♦ | @Ronnie - there is definitely a relation to fibrations, but Jean Benabou would be furious if I didn't say that one can use what he calls distributors (but almost everyone else calls profunctors) to deal with this issue (and these have a longer history). There is a property of an anafunctor called saturation, and saturated anafunctors between categories are equivalent to representable distributors/profunctors, so you can approach it from either side. However, you don't need the relation between the two to recover the sort of thing you are thinking of using anafunctors. | |
| Dec 12, 2012 at 17:58 | comment | added | Almeo Maus | Thank you very much for your answer! I will take time to understand the notion, that seems to help define those functors "defined up to (canonical) isomorphisms". – Almeo Maus 0 secs ago | |
| Dec 12, 2012 at 11:32 | comment | added | Ronnie Brown | @david: Has this idea been ap[plied to fibrations of categories replacing the notion of cleavage? I recall Benabou was not keen on assuming that fibrations had a cleavage. | |
| Dec 11, 2012 at 23:44 | history | answered | David Roberts♦ | CC BY-SA 3.0 |