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Operads, algebras and modules. (English) Zbl 0879.18001

Loday, Jean-Louis (ed.) et al., Operads: Proceedings of renaissance conferences. Special session and international conference on moduli spaces, operads, and representation theory/operads and homotopy algebra, March 1995/May–June 1995, Hartford, CT, USA/Luminy, France. Providence, RI: American Mathematical Society. Contemp. Math. 202, 15-31 (1997).
This is the text of a talk given by the author in a conference on moduli spaces, operads, and representation theory/operads and homotopy algebra at Hartford, CT and Luminy in 1995. It is largely based on Part I and II of the article by I. Kriz and J. P. May, “Operads, algebras, modules and motives” [Astérisque 233 (1995; Zbl 0840.18001)], and to which the interested reader is referred for details. The text contains seven sections: 1. The definitions of operads, algebras and modules. 2. Monadic reinterpretation of algebras. 3. The specialization to algebraic operads. 4. Algebraic operads associated to topological operads. 5. Operads, loop spaces, \(n\)-Lie algebras, and \(n\)-braid algebras. 6. Homology operations in characteristic \(p\). 7. A conversion theorem. Moreover, there is a “handout” of definitions reproduced earlier on page 1 of the same volume as the present paper. It might be of help to the not so interested reader who only wants to know what the objects are which are studied in the theory of operads.
For the entire collection see [Zbl 0855.00018].

MSC:

18-02 Research exposition (monographs, survey articles) pertaining to category theory
55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
18C99 Categories and theories
18D99 Categorical structures
55P35 Loop spaces
55S12 Dyer-Lashof operations
55U99 Applied homological algebra and category theory in algebraic topology
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