Izvorni znanstveni članak

https://doi.org/10.3336/gm.44.1.08

Bimorphisms of a pro*-category

Nikola Koceić Bilan orcid.org/0000-0003-4430-0091 ; Department of Mathematics, University of Split, Split, Croatia

Sažetak

Every morphism of an abstract coarse shape category Sh(C, D)* can be viewed as a morphism of the category pro*-D (defined on the class of inverse systems in D), where D is dense in C. Thus, the study of coarse shape isomorphisms reduces to the study of isomorphisms in the appropriate category pro*-D. In this paper bimorphisms in a category pro*-D are considered, for various categories D. We discuss in which cases pro*-D is a balanced category (category in which every bimorphism is an isomorphism). We are interested in the question whether the fact that one of the categories: D, pro-D and pro*-D is balanced implies that the other two categories are balanced. It is proved that if pro*-D is balanced then D is balanced. Further, if D admits sums and products and pro*-D is balanced then pro-D is balanced. In particular, pro*-C is balanced for C = Set (the category of sets and functions) and C = Grp (the category of groups and homomorphisms).

Ključne riječi

Category; monomorphism; epimorphism; bimorphism; balanced category; pro-categories; topological space; polyhedron

Hrčak ID:

36949

URI

https://hrcak.srce.hr/36949

Datum izdavanja:

21.5.2009.

Posjeta: 1.218 *