On the operads of J.P. May. (English) Zbl 1082.18009
This is a reprint of a manuscript submitted in 1972 and never published. Its complete aspect and point of view give a present interest.
Working on iterated loop spaces, J. P. May introduces operads and shows that each operad gives rise to a monad on the category of pointed Hausdorff spaces. There is a close formal similarity between operads and clubs introduced in Kelly’s work on coherence problem in categories: each club gives rise to a monad on \({\mathcal C}at\).
The purpose of the paper is to throw light on operads from the categorical point of view by defining them in this greater generality and by showing abstractly why they give rise to monads.
Working on iterated loop spaces, J. P. May introduces operads and shows that each operad gives rise to a monad on the category of pointed Hausdorff spaces. There is a close formal similarity between operads and clubs introduced in Kelly’s work on coherence problem in categories: each club gives rise to a monad on \({\mathcal C}at\).
The purpose of the paper is to throw light on operads from the categorical point of view by defining them in this greater generality and by showing abstractly why they give rise to monads.
Reviewer: Georges Hoff (Villetaneuse)
MSC:
| 18D50 | Operads (MSC2010) |
| 18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
| 18D20 | Enriched categories (over closed or monoidal categories) |
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 55P48 | Loop space machines and operads in algebraic topology |
