Glasnik matematički, Vol. 44 No. 1, 2009.
Original scientific paper
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
Abstract
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).
Keywords
Category; monomorphism; epimorphism; bimorphism; balanced category; pro-categories; topological space; polyhedron
Hrčak ID:
36949
URI
Publication date:
21.5.2009.
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