Action of derived automorphisms on infinity-morphisms
K-Theory and Homology
2015-06-02 v3
Abstract
In this paper we investigate how to simultaneously change homotopy algebras of a certain type and a corresponding infinity morphism between them, and show that this can be done in a homotopically unique way. More precisely, for a reduced cooperad C, given \Omega(C)-algebras V and W and an infinity-morphism U from V to W, for any derivation \phi of \Omega(C) we produce new \Omega(C)-algebras V' and W' and a new infinity-morphism U' between them, that are unique up to homotopy. Operads play the central role in answering this question, in particular a 2-colored operad Cyl(C) that governs pairs of homotopy algebras and infinity-morphisms between them.
Keywords
Cite
@article{arxiv.1305.4699,
title = {Action of derived automorphisms on infinity-morphisms},
author = {Brian Paljug},
journal= {arXiv preprint arXiv:1305.4699},
year = {2015}
}
Comments
Final version, to be published in the Journal of Homotopy and Related Structures