2013/05/31 by Brian Paljug · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.KT
paper · pdf · doi:10.1007/s40062-015-0104-0
Final version, to be published in the Journal of Homotopy and Related Structures
openalex publication_date 2015/03/24 · arxiv created 2015/06/01 · arxiv updated 2015/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 Ω(C)-algebras V and W and an infinity-morphism U from V to W, for any derivation ϕof Ω(C) we produce new Ω(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.