Homotopical Algebra (Repost)
Daniel G. Quillen, "Homotopical Algebra"
1967 | pages: 160 | ISBN: 0387039147 | PDF | 3,8 mb
1967 | pages: 160 | ISBN: 0387039147 | PDF | 3,8 mb
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.
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