# PlanetPhysics/R Category

\newcommand{\sqdiagram}[9]{**Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}}**
}

## R-category definitionEdit

An * -category * is a *\htmladdnormallink{category* {http://planetphysics.us/encyclopedia/Cod.html} equipped with an -module structure on each *hom* set such that the composition is -bilinear}. More precisely, let us assume for instance that we are given a commutative ring with identity. Then a small -category--or equivalently an * -algebroid* -- will be defined as a category enriched in the monoidal category of -modules, with respect to the monoidal structure of tensor product. This means simply that for all objects of , the set is given the structure of an -module, and composition **Failed to parse (unknown function "\lra"): {\displaystyle A(b,c) \times A(c,d) \lra A(b,d)}**
is --bilinear, or is a morphism of -modules **Failed to parse (unknown function "\lra"): {\displaystyle A(b,c) \otimes_R A(c,d) \lra A(b,d)}**
.

## All SourcesEdit

^{[1]}^{[2]}