A simplicial $A_\infty$-operad acting on $R$-resolutions
Tilman Bauer, Assaf Libman
TL;DR
This paper develops a combinatorial model of an A-infinity-operad that acts on the cobar resolution of a simplicial set over a ring R, enhancing understanding of operadic actions in homotopical algebra.
Contribution
It introduces a new combinatorial model of an A-infinity-operad that acts directly on the cobar resolution, not just its total space.
Findings
Constructed a combinatorial A-infinity-operad model
Demonstrated operad acts on the cobar resolution
Provides tools for homotopical algebra applications
Abstract
We construct a combinatorial model of an A-infinity-operad which acts simplicially on the cobar resolution (not just its total space) of a simplicial set with respect to a ring R.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models