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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 $X_\xi$ ...
Jeff Strom's user avatar
  • 12.5k
9 votes
2 answers
988 views

Reference for homotopy colimit = total complex

I'm looking for a reference for the following fact: take a simplicial chain complex $ X:\Delta^{op}\to Ch_{\geq 0}(\mathcal A)$ for $\mathcal A$ a nice abelian category (say, cocomplete with enough ...
Maxime Ramzi's user avatar
  • 15.8k
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 ...
Ivan Di Liberti's user avatar
17 votes
10 answers
3k views

References for homotopy colimit

(1) What are some good references for homotopy colimits? (2) Where can I find a reference for the following concrete construction of a homotopy colimit? Start with a partial ordering, which I will ...
Kevin Walker's user avatar
  • 12.8k