Search Results

By curiosity, I would like to see an example of a model category with the underlying category locally presentable which is not accessible in this sense (and just in case: even by using Vopěnka's princ …

By browsing the list of open problems in Mark Hovey's book "Model categories", I came across the following one (Problem 8.3): find a model structure on topological spaces, with the same weak equivalen …

Question. Call a cubical model category a model category enriched over cubical sets equipped with a tensor product $X \otimes K$ and a cotensor product $X^K$ where $X$ is an object of the model categ …

In a combinatorial model category, every $\lambda$-filtered colimit is a homotopy colimit for $\lambda$ regular big enough. So for $\lambda$ regular big enough, every $\lambda$-filtered colimit of a d …

There is a well-known theorem for transporting a model category structure along a left adjoint $F:\mathcal{M}\to \mathcal{N}$ which is explained here and which is due to Sjoerd Crans. The difficult p …

I have the following situation: Three combinatorial model categories $\mathcal{K}_1, \mathcal{K}_2, \mathcal{K}_3$ such that all objects are fibrant (so no need to bother with the fibrant replaceme …

Consider the discrete combinatorial model structure on the category of $\Delta$-generated spaces: all maps are cofibrations and fibrations and the weak equivalences are the homeomorphisms. Applying Pr …

By abstract construction of a combinatorial model category, I mean starting from a locally presentable category satisfying some assumptions, e.g. equipped with a cylinder or a cocylinder satisfying so …

Consider a functor between small categories $i:\mathcal{A}\to \mathcal{B}$ which is faithful, not full, and bijective on objects. Consider a functor $F:\mathcal{A}\to \mathcal{M}$ where $\mathcal{M}$ …

Consider the Reedy category $2\rightarrow 1 \leftarrow 0$. Consider a map of diagrams of topological spaces $D\to E$ over this Reedy category: The maps which are fibrations are depicted with the symb …

Take a topologically enriched small category $\mathcal{P}$ and the category of enriched diagrams of spaces $[\mathcal{P},\mathrm{Top}]_0$. We work with the category of $\Delta$-generated spaces equipp …

I would like to know how to cite this theorem (which has a quite surprising consequence): A model category $\mathcal{M}$ is right proper if and only if for any weak equivalence $f:A\to B$, the Q …

Question. Is it true that to check that a model category is right proper, it suffices to check the property for weak equivalences with fibrant codomain ? (if the domain is also fibrant, the pullback i …

Let $I$ be a small category and $\mathcal{K}$ be a combinatorial model category. Is it known a model category structure on the functor category $\mathcal{K}^I$ such that a map of diagrams $D\to …

I read in nLab : Every cofibrantly generated model category structure can be lifted to that of an algebraic model category. It is not clear whether or not this is true for any accessible model categor …