Timeline for What are the advantages of simplicial model categories over non-simplicial ones?

6 events

when toggle format	what		by	license	comment
Mar 22, 2019 at 21:17	comment	added	Simon Henry		Yes, that is nice ! the example I mentioned actually worked essentially the same way, but with more "level" than justs two, which makes the combinatorics involved a lot more complicated.
Mar 22, 2019 at 20:50	comment	added	Alexander Campbell		(...) exists no model structure left-induced along the "free" functor Gph $\to$ Cat: for instance, the morphism $1+1 \to 1$ (where 1 is the graph with a single vertex and no edges) does not factorise as a "cofibration" (i.e. monomorphism) followed by a "weak equivalence".
Mar 22, 2019 at 20:46	comment	added	Alexander Campbell		A simple example of a category of algebraically cofibrant objects on which the left-induced model structure does not exist is as follows. There is a (cof. gen.) model structure on Cat in which a functor is a weak equivalence iff its poset-reflection is an isomorphism, and for which the pair of morphisms $0 \to 1$ and $1 + 1 \to \{0<1\}$ form a set of generating cofibrations. The cofibrant replacement comonad generated by this set is the "free category" comonad on Cat, whose category of coalgebras is equivalent to the category Gph of (directed) graphs. But on Gph there (...)
Mar 22, 2019 at 17:47	history	edited	Simon Henry	CC BY-SA 4.0	added 75 characters in body
Mar 22, 2019 at 16:21	history	edited	Simon Henry	CC BY-SA 4.0	added 244 characters in body
Mar 22, 2019 at 16:13	history	answered	Simon Henry	CC BY-SA 4.0