Glasnik Matematicki, Vol. 51, No. 2 (2016), 255-306.

THE SHAPES IN A CONCRETE CATEGORY

Nikica Uglešić

University of Zadar, Pavlinovićeva 1, 23000 Zadar, Croatia
e-mail: nuglesic@unizd.hr

Abstract.   We show under what conditions, and how, one can obtain a shape theory (various shape theories) in a concrete category. The technique is, roughly speaking, reduced to the quotients by congruences providing the objects of lower cardinalities. The application yields the new (coarser) classifications in every concrete category which admits sufficiently many non-trivial quotients. Thus, the ordering, (ultra)pseudometric, uniform and topological structures, as well as many algebraic and mixed (multi-) structures, give rise to interesting results.

2010 Mathematics Subject Classification.   03E99, 06A99, 16D99, 16S99, 20B07, 46A99, 54B15, 54B30, 54C56, 54E99, 55P55.

Key words and phrases.   (pointed) set, partially ordered set, (ultra)pseudometric space, topological space, monoid, group, ring, module, vector space, equivalence relation, congruence, (infinite) cardinal, concrete category, quotient object, dimension, expansion, pro-category, shape category.


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DOI: 10.3336/gm.51.2.01


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