Semimodule Enrichment

A category with biproducts is enriched over (commutative) additive monoids. A category with tensor products is enriched over scalar multiplication actions. A symmetric monoidal category with biproducts is enriched over semimodules. We show that these extensions of enrichment (e.g. from hom-sets to homsemimodules) are functorial, and use them to make precise the intuition that "compact objects are finitedimensional" in standard cases.

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Chris Heunen
• Keywords: Additive Monoids, ENTCS 2008, Scalar Multiplication Actions, Symmetric Monoidal Category