Operations on triple cohomology. (English) Zbl 0647.18003
Let (T,\(\mu\),\(\eta)\) be a triple on the category of R-modules. Given T- algebras AT\(\to A\) and BT\(\to B\), the author considers the non- homogeneous complex
\[
0 \to (A,B) \to (AT,B) \to (AT^ 2,B) \to ...
\]
enriched over the category of coalgebras. The circle product, satisfying a Leibniz formula on its cochains is defined. It implies the known examples and extends them to algebras of most general character [cf. M. Gerstenhaber, Ann. Math., II. Ser. 78, 267-288 (1963; Zbl 0131.273)].
Reviewer: M.Golasiński
MSC:
| 18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
| 13D05 | Homological dimension and commutative rings |
| 18G50 | Nonabelian homological algebra (category-theoretic aspects) |
| 55U15 | Chain complexes in algebraic topology |
Citations:
Zbl 0131.273References:
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