Internal precategories relative to split epimorphisms

Details Internal precategories relative to split epimorphisms Internal precategories relative to split epimorphisms

2009-03-02

arxiv.org/abs/0903.0333v1

Mathematics

Category Theory

31 pages

Scientific paper

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.

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