RT Journal Article
T1 Monomorphisms and epimorphisms in pro-categories
A1 Dydak, J.
A1 Romero Ruiz del Portal, Francisco
AB A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. We give haracterizations of monomorphisms (respectively, epimorphisms) in pro-category pro-C, provided C has direct sums (respectively,pushouts).Let E(C) (respectively, M(C)) be the subcategory of C whose morphisms are epimorphisms (respectively, monomorphisms)of C. We give conditions in some categories C for an object X of pro-C to be isomorphic to an object of pro-E(C) (respectively,pro-M(C)).A related class of objects of pro-C consists of X such that there is an epimorphism X→P ∈ Ob(C) (respectively, a monomorphismP  Ob(C) →X). Characterizing those objects involves conditions analogous (respectively, dual) to the Mittag–Leffler property. One should expect that the object belonging to both classes ought to be stable. It is so in the case of pro-groups. The natural environment to discuss those questions are balanced categories with epimorphic images. The last part of the paper deals with that question in pro-homotopy.
PB Elsevier Science
SN 0166-8641
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50343
UL https://hdl.handle.net/20.500.14352/50343
LA eng
NO NSF Ministry of Science and Education of Spain
NO MEC
DS Docta Complutense
RD 7 may 2025