2023/01/20 by Yang Mo, Mo, Yang
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2301.08462
openalex publication_date 2023/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simply colored coalgebra is a coassociative counital coalgebra C over an arbitrary ring R, which can be decomposed into a direct sum of two R-modules: one generated by set-like elements and another consisting of conilpotent elements. Our main result is the equivalence between simply colored coalgebras over a field k and pointed coalgebras with a choice of splitting of its coradical. Additionally, we also prove that the category of simply colored coalgebras is both complete and cocomplete.