The isofibrations are the fibrations of the canonical model structure of the category of small categories. If I call fibration of small categories the same notion by removing the word isomorphism, i.e. a functor $p:E\to B$ such that every map $p(e)\to b$ can be written as $p(\psi):p(e)\to p(e')$, is this class of maps the class of fibrations of a fibration category or a model category on small categories ?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ I’m not sure I’d call that a fibration. Anyway you might be interested in Moser and Sarazola. $\endgroup$– Tim CampionCommented Jan 5 at 16:32
-
$\begingroup$ Offhand, I don't know the answer, but here are some helpful observations. The folk model structure is the ONLY model structure on Cat whose weak equivalences are the equivalences of categories (see Sec 9.1 of Scott Balchin's book for a published reference of this); so you'll need fewer w.e.'s. And the isofibrations are characterized by the RLP wrt $pt\to E$ where E is the free walking arrow isomorphism. It seems a first step is to think about characterizing your fibrations via RLP, but with respect to what morphism(s)? $\endgroup$– David WhiteCommented Jan 6 at 22:53
-
$\begingroup$ @DavidWhite they are characterized by the rlp with respect to the the left 1-horn inclusion $\Delta^0\to\Delta^1$ $\endgroup$– Tim CampionCommented Jan 7 at 0:37
Add a comment
|