2009/03/02 by Nelson Martins-Ferreira, N. Martins-Ferreira, Martins-Ferreira, N.
Mathematics · #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras #math.CT
paper · pdf · doi:10.48550/arxiv.0903.0333
31 pages
arxiv created 2009/03/02 · openalex publication_date 2009/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given category B we are interested in studying internal categorical structures in B. This work is the starting point, where we consider reflexive graphs and precategories (i.e., for the purpose of this note, a simplicial object truncated at level 2). We introduce the notions of reflexive graph and precategory relative to split epimorphisms. We study the additive case, where the split epimorphisms are "coproduct projections", and the semi-additive case where split epimorphisms are "semi-direct product projections". The result is a generalization of the well known equivalence between precategories and 2-chain complexes. We also consider an abstract setting, containing, for example, strongly unital categories.