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Oct, 2020
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Homotopical Algebra

Those who have been studying algebraic topology often realize that some operations on spaces and continous maps look similar to algebraic constructions. For example, localizations of spaces , homotopy (co)limits , and calculus of functors .

We collect such “algebraic operations on spaces” in this page. The term “homotopical algebra” is used in this sense, although it is the title of Quillen’s book [ Qui67 ] in which he introduced the notion of closed model category . The term “homotopical algebra” is often used for theory of model categories. Nowadays, the notion of model categories is very popular, I guess no confusion arises if the term “homotopical algebra” is used in the above sense.

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