Search Results

I believe what you are after is the notion of "elegant Reedy category" This sort of things isn't true for a general Reedy category, but for an elegant one $R$ (see the link for the definition) if $\ma …

Let $G$ be a discrete group. Consider the category of $G$-simplicial sets endowed with the injective model structure, i.e. cofibrations are the injective maps and weak equivalences are the maps which …

I am looking for an example where a transferred model structure fails to exist, even if one is willing to work with semi-model category. But let me be more precise: Let's say I have a combinatorial mo …

Actually, you can, and you don't need accessibility (local presentability of the underlying category is enough). Under your assumption, for each $i:A \to B$ a generating cofibration, take $B \coprod_A …

As mentioned by David White in the comment, I've recently proved that left induced model structure exists (without any kind of large cardinal axiom) for any "tractable" class of cofibrations on a loc …

I'm still confused by the question when $n>0$: $\pi_n^{\tau} X $ are already groups, so applying the group completion functor do not do anything to them, and, even in the catagory of spaces, I have ne …

In short there isn't: the problem is that if you just have globular sets - and if you want $k$-cells to model $k$-arrows following the globular structure - then globular sets have no way of expressing …

I have recently been thinking about left and right semi-model categories and in which case they can be promoted to Quillen model structure, and I have come to the conclusion that that absolutely all t …

Regarding (1) : A) Every model category has an associated $\infty$-category, obtained for example by taking the Dwyer-Kan localization at the class of all equivalence, (But there are other more expli …

I'm looking for a Quillen model category which model the $2$-category of 'small category with finite limits (and functors between them preserving finite limits)': Left proper, right proper, Enriched …

For a model category $C$, I'm denoting $h_\infty(C)$ the associated $\infty$-category (for example its Dwyer-Kan localization at weak equivalences, or if $C$ is simplicial the simplicial nerve of the …

This is probably not a full answer to your question, but I think it is a remark worth to make: It is actually a couple of remarks: 1)If you have a weak factorization system where either the left cla …

It is not the case: the terminal semi-simplicial set $1$ is obviously fibrant but as I will show below the geometric product $1 \otimes 1$ is not fibrant. 1) What does $1 \otimes 1$ look like ? So, $1 …

I believe the main reasons enriched model category are simpler boils down to: Tensoring and co-tensoring by $\Delta[1]$ gives very well behaved path objects and cylinder objects adjoint to each other …

Let $\mathcal{T}= sh(C,J)$ a Grothendieck topos of sheaves over a (ordinary) site. One endows the category of simplicial presheaves over $C$ with the "Rezk-Lurie" model structure: that is we start wi …