Algebra+Homotopy=Operad
Algebraic Topology
2012-02-16 v1 Mathematical Physics
Algebraic Geometry
Category Theory
K-Theory and Homology
math.MP
Quantum Algebra
Abstract
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in Algebra, Geometry, Topology, and Mathematical Physics. (This text is accessible to any student knowing what tensor products, chain complexes, and categories are.)
Cite
@article{arxiv.1202.3245,
title = {Algebra+Homotopy=Operad},
author = {Bruno Vallette},
journal= {arXiv preprint arXiv:1202.3245},
year = {2012}
}
Comments
59 figures, 31 exercices, 43 pages