| Title:
|
Effective homology for homotopy colimit and cofibrant replacement (English) |
| Author:
|
Filakovský, Marek |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
273-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X \colon \mathcal{I}\rightarrow \mbox{sSet}$ such that each simplicial set $X(i)$ has effective homology, we present an algorithm computing the homotopy colimit $\mbox{hocolim}\,X$ as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement $X^{\mbox{cof}}$ of $X$ as a diagram with effective homology. This is applied to computing of equivariant cohomology operations. (English) |
| Keyword:
|
homotopy colimit |
| Keyword:
|
cofibrant replacement |
| Keyword:
|
effective homology |
| Keyword:
|
equivariant |
| MSC:
|
55N91 |
| MSC:
|
55U15 |
| idZBL:
|
Zbl 06487012 |
| idMR:
|
MR3303777 |
| DOI:
|
10.5817/AM2014-5-273 |
| . |
| Date available:
|
2015-01-07T14:53:36Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144070 |
| . |
| Reference:
|
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