The structure of simply colored coalgebras

Yang Mo

The structure of simply colored coalgebras

Algebraic Topology 2023-09-26 v2 Mathematical Physics math.MP Quantum Algebra

Authors: Yang Mo

Abstract

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.

Keywords

simply colored coalgebra coassociative coalgebra set-like elements conilpotent elements pointed coalgebra coradical

Cite

@article{arxiv.2301.08462,
  title  = {The structure of simply colored coalgebras},
  author = {Yang Mo},
  journal= {arXiv preprint arXiv:2301.08462},
  year   = {2023}
}

Comments

rewrite the abstract and introduction. Also, clarify some definitions and results based on advice from referees. To appear in Contemporary Math volume Higher Structures in Topology, Geometry and Physics. All comments are welcome

The structure of simply colored coalgebras

Abstract

Keywords

Cite

Comments

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