2010/12/15 by Stefan Forcey, Forcey, Stefan, Aaron Lauve +3
Mathematics · #05E05 #16W30 #18D50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CO #msc:05E05 #msc:16W30 #msc:18D50
paper · pdf · doi:10.48550/arxiv.1012.3483
22 pages
arxiv created 2010/12/15 · openalex publication_date 2010/12/15 · arxiv updated 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and in the theory of species. We prove that the composition of two cofree coalgebras is again cofree, and we give sufficient conditions that ensure the composition is a one-sided Hopf algebra. We show these conditions are satisfied when one coalgebra is a graded Hopf operad D and the other is a connected graded coalgebra with coalgebra map to D. We conclude by computing the primitive elements for compositions of coalgebras built on the vertices of multiplihedra, composihedra, and hypercubes.