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Results tagged with model-categories
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user 23571
A model category is a category equipped with notions of weak equivalences, fibrations and cofibrations allowing to run arguments similar to those of classical homotopy theory.
15
votes
Accepted
Is geometric realization of the total singular complex of a space homotopy equivalent to the...
The map from the (realization of the) singular complex of a space $X$ to $X$ is a homotopy equivalence if and only if $X$ is homotopy equivalent to a CW complex, so to get examples where the map is no …
- 20k
5
votes
Five lemma in HoTop* and arbitrary pointed model categories
Here are some comments on Tyler's nice example, which answers the question of whether a map from a CW complex $Z$ to itself is a homotopy equivalence if it restricts to a homotopy equivalence from a s …
- 20k