Fraction, Restriction and Range Categories from Non-Monic Classes of Morphisms

20 Oct 2019 Hosseini S. N. Nasab A. R. Shir Ali Tholen W.

For a composition-closed and pullback-stable class S of morphisms in a category C containing all isomorphisms, we form the category Span(C,S) of S-spans (s,f) in C with first "leg" s lying in S, and give an alternative construction of its quotient category C[S^{-1}] of S-fractions. Instead of trying to turn S-morphisms "directly" into isomorphisms, we turn them separately into retractions and into sections in a universal manner, thus obtaining the quotient categories Retr( C,S) and Sect(C,S)... (read more)

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