The Koszul Complex is the Cotangent Complex
Copyright policy )The Koszul Complex is the Cotangent Complex
We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent complex, involved in the cohomology theory of algebras over an operad, generalizes the Koszul complex.
23 pages
André-Quillen cohomologie, Koszul duality, 18D50; 16S37, K-Theory and Homology (math.KT), [MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-KT] Mathematics [math]/K-Theory and Homology [math.KT], 16S37, 18D50, Mathematics - K-Theory and Homology, Cotangent complex, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology
André-Quillen cohomologie, Koszul duality, 18D50; 16S37, K-Theory and Homology (math.KT), [MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-KT] Mathematics [math]/K-Theory and Homology [math.KT], 16S37, 18D50, Mathematics - K-Theory and Homology, Cotangent complex, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology
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