Glasnik Matematicki, Vol. 42, No.2 (2007), 309-318.

ORTHOGONALITY, SATURATION AND SHAPE

Luciano Stramaccia

Dipartimento di Matematica e Informatica, Università di Perugia, via Pascoli, 06123 Perugia, Italia
e-mail: stra@dipmat.unipg.it

Abstract.   The class of shape equivalences for a pair (C, K) of categories is the orthogonal of K, that is Σ = K perp. Then Σ is internally saturated (Σ = Σtop perp). On the other hand, every internally saturated class of morphisms Σ subset Mor(C), is the class of shape equivalences for some pair (C, K). Moreover, every class of shape equivalences Σ enjoys a calculus of left fractions and such a fact allows one to use techniques from categories of fractions to obtain conditions for Σtop to be reflective or proreflective in C.

2000 Mathematics Subject Classification.   18A40, 18A25, 54B30, 55P55.

Key words and phrases.   Orthogonality, internal saturation, calculus of fractions, shape, shape equivalences.

Full text (PDF) (free access)

DOI: 10.3336/gm.42.2.06

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