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Daniel G. Quillen

Homotopical algebra or non-linear homological algebra is the generalization of homological algebra to arbitrary categories which results by considering a simplicial object as being a generalization of a chain complex. The first step in the theory was presented in [5], [6], where the derived functors of a non-additive functor from an abelian category A with enough projectives to another category B were constructed. This construction generalizes to the case where A is a category closed under finite limits having sufficiently many protective objects, and these derived functors can be used to give a uniform definition of cohomology for universal algebras. In order to compute this cohomology for commutative rings, the author was led to consider the simplicial objects over A as forming the objects of a homotopy theory analogous to the homotopy theory of algebraic topology, then using the analogy as a source of intuition for simplicial objects.

Idioma Inglés
Publicación 1967
Editorial Springer
Categoría Ciencias


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