Additive Categories
In mathematics, specifically in category theory, an additive category is a preadditive category C such that all finite collections of objects A1, … , An of C have a biproduct A1 ⊕ ⋯ ⊕ An in C.
A category C is preadditive if all its hom-sets are Abelian groups and composition of morphisms is bilinear; in other words, C is enriched over the monoidal category of Abelian groups. A biproduct in a preadditive category is both a finitary product and a finitary coproduct.
Read more about Additive Categories: Definition, Examples, Internal Characterisation of The Addition Law, Matrix Representation of Morphisms, Additive Functors, Special Cases
Famous quotes containing the word categories:
“All cultural change reduces itself to a difference of categories. All revolutions, whether in the sciences or world history, occur merely because spirit has changed its categories in order to understand and examine what belongs to it, in order to possess and grasp itself in a truer, deeper, more intimate and unified manner.”
—Georg Wilhelm Friedrich Hegel (1770–1831)