All Questions
Tagged with limits-and-colimits model-categories
9 questions
4
votes
0
answers
88
views
Homotopy colimits in subcategories of combinatorial model categories
We know that, in a combinatorial simplicial model category $\mathbf{M}$, we can find a regular cardinal $\lambda$ large enough that all $\lambda$-filtered homotopy colimits can be computed as strict ...
- 1,071
9
votes
0
answers
393
views
When is an increasing union a colimit?
Let's consider a diagram $\Phi: \lambda \to \mathcal{T}_*$
$$
X_0 \to X_1 \to \cdots \to X_\xi \to X_{\xi+1} \to \cdots
$$
of pointed spaces,
indexed by some ordinal $\lambda$, in which each $X_\xi$ ...
- 12.5k
7
votes
4
answers
1k
views
Existence of homotopy limits and colimits in model categories
I am not an expert, thus I apologize if my question is very naive. Let $\mathsf{M}$ be a model category (I do not assume any functoriality on the factorization),
Q1. Is there a reference where it is ...
- 9,111
9
votes
1
answer
344
views
Explicit calculations of small homotopy limits of CDGAs
I would like to carry out explicit calculations of homotopy limits of certain simple diagrams of CDGAS. My set-up is the following : I have a finite graded poset $R$ with minimal element $0$ and a ...
- 2,751
3
votes
0
answers
361
views
Which reflexive coequalizer diagrams are projectively cofibrant?
Consider the walking reflexive pair category W,
which consists of two objects 0 and 1 and three generating
morphisms f: 0→1, g: 0→1, and h: 1→0
satisfying the relation fh=gh=id₁.
Consider the ...
- 37.8k
4
votes
1
answer
761
views
When do reflexive coequalizers preserve weak equivalences?
In my work I've run into the following situation. In a model category, I have two reflexive coequalizers $A_i \stackrel{\to}{\to} B_i \to C_i$ and a map of diagrams which is levelwise a weak ...
- 30.3k
10
votes
2
answers
863
views
Fubini theorem for hocolim
I wanted to ask the following question,
Suppose $\mathbf{M}$ a cofibrantly generated model category and $I,~J$ two small categories. Suppose that $F:J\rightarrow \mathbf{M}^{\mathrm{I}}$ is a functor. ...
- 1,974
8
votes
3
answers
2k
views
Is the category of small categories locally presentable?
I was wondering whether the various model structures on the category of small categories are combinatorial. I think that the ones I know are at least cofibrantly generated. In order to be ...
- 15.2k
9
votes
1
answer
814
views
How does Berger-Moerdijk's relative Boardman-Vogt work?
In "The Boardman-Vogt resolution of operads in monoidal model categories," the authors construct factorizations of sufficiently nice operad maps $P\to Q$ into a cofibration followed by a weak ...
- 4,588