nLab
tensor product of presentable (infinity,1)-categories

Contents

Idea

The tensor product of presentable (,1)(\infty,1)-categories is the product in the symmetric monoidal (infinity,1)-category of presentable (infinity,1)-categories. See there for more details.

This is the (,1)(\infty,1)-category CDC \otimes D which is ‘the universal recipient of a bilinear functor’ from C×DC \times D. Here, we think of coproducts in CC and DD as addition, and then if a functor C×DEC \times D \to E preserves colimits in each variable, in particular it preserves coproducts and so is ‘bilinear’. Such a bilinear functor will factor uniquely (in a homotopic sense) through a universal bilinear functor C×DCDC \times D \to C \otimes D, just like for bilinear maps and tensor products of abelian groups.

Revised on January 17, 2013 01:29:01 by Urs Schreiber (203.116.137.162)