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Results tagged with model-categories
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user 2039
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.
38
votes
Do we still need model categories?
One nice feature of model categories is that you can speak also of the non-bifibrant objects (which is not longer possible, once you passed to the corresponding infinity-category). A few examples wher …
- 12.1k
38
votes
Why do we need model categories?
Model categories capture the idea that in many cases you resolve an object by an equivalent object that is better behaved. The standard example is replacing a chain complex by a chain complex of proje …
- 12.1k
51
votes
What is modern algebraic topology(homotopy theory) about?
While I think that Andre is right in saying that homotopy theory (or algebraic topology) is ready to study everything that fits into the framework of abstract homotopy theory, some things have still a …