Reflective and coreflective subcategories

Given any additive category C with split idempotents, pseudokernels and pseudocokernels, we show that a subcategory B is coreflective if, only it precovering, closed under direct summands each morphism in has pseudocokernel belongs to B. We apply this result its dual to, among others, preabelian pretriangulated categories. As consequence, of it, precovering taking cokernels. On the other hand, if then invariant suspension functor cones. These are extensions well-known results for AB3 abelian triangulated categories, respectively. By-side applications these allow us: a) To characterize subcategories given which have set generators themselves abelian, exact or module categories; b) extend categories over arbitrary small preadditive Gabriel De la Peña stating all fully bireflective; c) that, Grothendieck category, limit closure finitely presented objects subcategory.