与分裂满射有关的内预范畴
Internal precategories relative to split epimorphisms
摘要：
对于一个给定的范畴B，我们感兴趣的是研究B中的内部范畴结构。这项工作是起点，在那里我们考虑自反图和precategories（即，为了本说明的目的，单纯对象在级别2处被截断）。我们引入了自反图和与分裂满态相关的预范畴的概念。研究了分裂满态是“余积投影”的加法情形和分裂满态是“半直积投影”的半加法情形。其结果推广了前范畴与2-链复形之间的等价性。我们也考虑一个抽象的设置，包含，例如，强单位范畴。
英文摘要：
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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