All Questions
5 questions
8
votes
1
answer
440
views
Model categories as a tool to resolve size issues for localizing categories
I have a rather basic question about one motivation for introducing model categories in David White's notes, as a possible way to overcome troubles with size issues appearing when localizing a ...
1
vote
1
answer
177
views
Colocal Objects in Enriched Bousfield Colocalizations
Let $C$ be a $V$-model category, and $\mathcal{K}$ a set of objects of $C$.
Let me denote (derived) simplicial homotopy function complexes by $\text{Dmap}$
and derived $V$-function complexes by $\text{...
10
votes
1
answer
763
views
Example of a saturated class of morphisms which is not _obviously_ saturated?
By "saturated class of morphisms" in a category $\mathcal{C}$, I mean a subcategory $\mathcal{W} \subset \mathcal{C}$ such that the image of $\mathcal{W}$ in $\mathcal{C}[\mathcal{W}^{-1}]$ consists ...
5
votes
0
answers
225
views
Weak equivalences of left Bousfield localizations
Suppose C is a complete and cocomplete category with two model structures (C0,F0,W0) and (C1,F1,W1) such that C0⊃C1, F0⊂F1, W0⊂W1.
If necessary, the model structures can be assumed to be simplicial, ...
10
votes
2
answers
824
views
Is there a notion of a “model category which admits left Bousfield localization?”
At a conference not too long ago I gave a talk on (left) Bousfield localization and was asked an interesting question afterwards. The question was whether I knew any examples of model categories which ...