Editing Preadditive category (section)

== {{mvar|R}}-linear categories ==

More generally, one can consider a category {{mvar|C}} enriched over the monoidal category of [[module (mathematics)|modules]] over a [[commutative ring]] {{mvar|R}}, called an '''{{mvar|R}}-linear category'''. In other words, each [[hom-set]] <math>\text{Hom}(A,B)</math> in {{mvar|C}} has the structure of an {{mvar|R}}-module, and composition of morphisms is {{mvar|R}}-bilinear.

When considering functors between two {{mvar|R}}-linear categories, one often restricts to those that are {{mvar|R}}-linear, so those that induce {{mvar|R}}-linear maps on each hom-set.