Naturally full functors in nature

Semiseparable functors

In this paper we introduce and investigate the notion of semiseparable functor. One of its first features is that it allows a novel description of separable and naturally full functors in terms of faithful and full functors, respectively. To any semiseparable functor we attach an invariant, given by an idempotent natural transformation, which controls when the functor is separable and yields a characterization of separable functors in terms of (dual) Maschke and conservative functors. We prove that any semiseparable functor admits a canonical factorization as a naturally full functor followed …

Reflexive functors of modules in Commutative Algebra

Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.

论（自然）半满与（半）可分半函子

On (naturally) semifull and (semi)separable semifunctors

本文将满性、忠实性、可分性与自然满性推广到半函子，引入半满及自然半满概念，并用半伴随的单位、余单位半分裂条件加以刻画，证明 Rafael 型与 Maschke 型定理。