کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661047 | 1344397 | 2008 | 12 صفحه PDF | دانلود رایگان |
Given a category pair (C,D), where D is dense in C, the abstract coarse shape category was recently founded. It is realized via the category pro*-D defined on the class of all inverse systems in D. In this paper monomorphisms and epimorphisms in the category pro*-C are considered, for various categories C. The characterizations of epimorphisms (monomorphisms) in the category pro*-C are given, provided C admits products (sums). Since, one may consider the category pro-C as a subcategory of pro*-C, we discuss in which cases an epimorphism (monomorphism) in pro-C is an epimorphism (monomorphism) in pro*-C as well. We answered this question affirmatively for a category C admitting products (sums). It is shown by examples that the answer is generally negative, i.e. there exists a certain category C and an epimorphism (monomorphism) in pro-C which is not an epimorphism (monomorphism) in pro*-C.
Journal: Topology and its Applications - Volume 155, Issue 16, 1 October 2008, Pages 1840-1851