Hinich, Vladimir Homological algebra of homotopy algebras. (English) Zbl 0894.18008 Commun. Algebra 25, No. 10, 3291-3323 (1997). If \(k\) is a ring and \(C(k)\) the category of unbounded complexes of \(k\)-modules, then there is a well structured homological (in fact homotopical) algebra defined on \(C(k)\). Replacing \(k\) by a d.g. algebra, the same result holds. This possibility of working with unbounded complexes is important if one wants to go beyond d.g. algebras to weak algebras in which associativity, etc. hold only up to higher homotopies. A convenient setting then is that of operads and operad algebras and in this paper the author shows that the usual theory extends with great simplicity to that very much more general setting. This enables the definition of cohomology of operad algebras and a corresponding cotangent complex to be defined. Reviewer: T.Porter (Bangor) Cited in 7 ReviewsCited in 112 Documents MSC: 18G55 Nonabelian homotopical algebra (MSC2010) 18G25 Relative homological algebra, projective classes (category-theoretic aspects) 18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads Keywords:tangent Lie algebra; homotopical algebra; operads; operad algebras PDFBibTeX XMLCite \textit{V. Hinich}, Commun. Algebra 25, No. 10, 3291--3323 (1997; Zbl 0894.18008) Full Text: DOI arXiv References: [1] Avramov L., Differential graded homological algebra (1991) [2] Bernstein J., Lecture note in Math 1578 (1994) [3] Bousfield A.K., Memoirs AMS 179 (1976) [4] DOI: 10.1215/S0012-7094-94-07608-4 · Zbl 0855.18006 [5] Hartshorne R., Lecture notes in Math 20 (1966) [6] Hinich V., Lecture notes in Math 20 pp 240– (1289) [7] Hinich V., Advances in Soviet Mathematics 16 pp 1– (1993) [8] Hinich V., Deformation theory and Lie algebra homology · Zbl 0919.17014 [9] Kriz I., Astensque 233 (1995) [10] Markl M., Models for operads · Zbl 0848.18003 [11] Quillen D., Lecture notes in Math 43 (1967) [12] DOI: 10.2307/1970725 · Zbl 0191.53702 [13] Quillen D., Proc. Symp. Pure Math pp 65– (1970) [14] Spaltenstein N., Compos. Math 65 pp 121– (1988) [15] DOI: 10.1016/0022-4049(85)90019-2 · Zbl 0576.17008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.