18 Feb
2009
18 Feb
'09
4:23 p.m.
Dear Category Theory gurus, In my reserach I have encountered the following problem. Let A be a full isomorphism-closed coreflective subcategory of a category C, G : C -> A be a coreflection. Let (E, M) be a factorization system for C-morphisms, such that class G(E) contains class of all A-isomorphisms and is contained in class of all A-retractions. Is any of the following statements correct: 1. If functor G preserves M, then it preserves E. 2. If any M-morphism is mono, then an M-morphism belongs to Mor(A) provided that its codomain belongs to Ob(A). Examples known to me satisfy both statements, but I fail to prove any. Thanks, Serge.