Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský

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arXiv · 1410.3396

Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský

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Abstract

We extend the notion of simplicial set with effective homology to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X \colon \mathcal{I} \to \mathsf{sSet}$ such that each simplicial set $X(i)$ has effective homology, we present an algorithm computing the homotopy colimit $\mathsf{hocolim} X$ as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement $X^\mathsf{cof}$ of $X$ as a diagram with effective homology. This is applied to computing of equivariant cohomology operations.

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BibTeX RIS

Marek Filakovský. 2014-10-13. Effective homology for homotopy colimit and cofibrant replacement. https://arxiv.org/abs/1410.3396

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