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Triangulated category - A triangulated category is a mathematical category satisfying some axioms that are based on the properties of a derived category. Some examples are the homotopy category of spectra, and the derived category of an abelian category.
Dual (category theory) - In category theory, an abstract branch of mathematics, the dual category or opposite category Cop of a category C is the category formed by reversing all the morphisms of C. That is, we take Cop to be the category with objects that are those of C, but with the morphisms from X ...
Preadditive category - In mathematics, specifically in category theory, a preadditive category is a category that is enriched over the monoidal category of abelian groups. In other words, the category C is preadditive if every hom-set Hom(A,B) in C has the structure of an abelian group, and composition of morphisms ...
2-category - In category theory, a 2-category is a category with "morphisms between morphisms". It can be formally defined as a category enriched over Cat (the category of categories and functors, with the monoidal structure induced by the composition).
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