Modules Over Operads And Functors
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Modules over Operads and Functors
This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.
Modules Over Operads and Functors
Author: Benoit Fresse
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-03-26
The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.
On Operads, Bimodules and Analytic Functors
Author: Nicola Gambino
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-09-25
The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.