Effective homology for homotopy colimit and cofibrant replacement
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.3396
 Bibcode:
 2014arXiv1410.3396F
 Keywords:

 Mathematics  Algebraic Topology;
 55U10;
 55N91
 EPrint:
 Archivum Mathematicum 050.5 (2014): 273286