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Algebraic theories in homotopy theory. (English) Zbl 1028.18001

The framework of Lawvere’s algebraic theories relaxed with the notion of homotopy algebras is convenient to describe various homotopy invariant structures on spaces. The relationship between strict and homotopy algebras is presented as a Quillen equivalence between model categories.

MSC:

18C10 Theories (e.g., algebraic theories), structure, and semantics
18G55 Nonabelian homotopical algebra (MSC2010)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
55U40 Topological categories, foundations of homotopy theory
55P99 Homotopy theory
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