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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.
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
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