We introduce and discuss the notion of a naturally full functor. The definition is similar to the definition of a separable functor; a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial version of a faithful functor. We study the general properties of naturally full functors. We also discuss when functors between module categories and between categories of comodules over a coring are naturally full.
Naturally Full Functors in Nature
ARDIZZONI, Alessandro;
2006-01-01
Abstract
We introduce and discuss the notion of a naturally full functor. The definition is similar to the definition of a separable functor; a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial version of a faithful functor. We study the general properties of naturally full functors. We also discuss when functors between module categories and between categories of comodules over a coring are naturally full.
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