2020/03/24 by J. P. May, May, J. P., Ruoqi Zhang +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2003.10934
openalex publication_date 2020/03/24 · openalex created_date 2020/04/03 · openalex updated_date 2026/07/28
We give a description of unital operads in a symmetric monoidal category as monoids in a monoidal category of unital Λ-sequences. This is a new variant of Kelly's old description of operads as monoids in the monoidal category of symmetric sequences. The monads associated to unital operads are the ones of interest in iterated loop space theory and factorization homology, among many other applications. Our new description of unital operads allows an illuminating comparison between the two-sided monadic bar constructions used in such applications and "classical" monoidal two-sided bar constructions. It also allows a more conceptual understanding of the scanning map central to non-abelian Poincaré duality in factorization homology.