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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
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4 votes
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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 ...
Giulio Lo Monaco's user avatar
3 votes
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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 ...
Dmitri Pavlov's user avatar