Tag Info

New answers tagged

1

The category $(A\downarrow \mathcal{M}\downarrow B)$ is not necessarily a model category, as it can fail to be complete or cocomplete (or both). For example, $(\{*\} \downarrow \mathsf{Set} \downarrow \varnothing)$ is not a model category: it is empty! There is no map from a singleton to the empty set. However one can define, for every $f : A \to B$, the ...


0

In the case that all isomorphisms in the model category are fibration, cofibration, and weak equivalences, (trivial cofibrations, fibrations) and (fibrations, trivial cofibrations) form factorization systems in the sense of Borceux: A factorization system in a category $\mathbf B$ is defined as a pair $(E, F)$ of classes of arrows in $\mathbf B$ such ...



Top 50 recent answers are included