标题： 半可分离函子和到收缩的条件 显示英文标题

标题： Semiseparable functors and conditions up to retracts

摘要： 在之前的一篇论文中，我们引入了半分离函子的概念。 在这里，我们继续研究这些函子与幂等（柯西）完成之间的关系。 为此，我们引入并研究了至可缩的（共）反射和双反射的概念。 我们证明了与一个其相关（共）单子为分离的伴随关系相关的（共）比较函子是至可缩的余反射（反射）。 这一事实使我们能够证明，一个右（左）伴随函子是半分离的当且仅当其相关的（共）单子是分离的，并且（共）比较函子是至可缩的双反射，扩展了X.-W. Chen在分离情况下的一个特征描述。 最后，我们提供了一个在预三角范畴框架下由P. Balmer获得的结果的半类比。 显示英文摘要

摘要： In a previous paper we introduced the concept of semiseparable functor. Here we continue our study of these functors in connection with idempotent (Cauchy) completion. To this aim, we introduce and investigate the notions of (co)reflection and bireflection up to retracts. We show that the (co)comparison functor attached to an adjunction whose associated (co)monad is separable is a coreflection (reflection) up to retracts. This fact allows us to prove that a right (left) adjoint functor is semiseparable if and only if the associated (co)monad is separable and the (co)comparison functor is a bireflection up to retracts, extending a characterization pursued by X.-W. Chen in the separable case. Finally, we provide a semi-analogue of a result obtained by P. Balmer in the framework of pre-triangulated categories.