In the category theory, an abstract subdivision of mathematics, a pre-additive category is a category enriched by the monoidal category of abelse groups. In other words, the category C is pre-additive if any hom-equation Him (A, B) in C has the structure of an abelse group, and the composition of morphs is bilinear across the integers.
A pre-additive category is also called an Ab category. The notation Ab stands for the category of abelse groups. Some authors have used the term additive category for pre-additive categories.
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