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Making factorizations compositive

Reinhard Börger (1991)

Commentationes Mathematicae Universitatis Carolinae

The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist.

Monomorphisms in spaces with Lindelöf filters

Richard N. Ball, Anthony W. Hager (2007)

Czechoslovak Mathematical Journal

𝐒𝐩𝐅𝐢 is the category of spaces with filters: an object is a pair ( X , ) , X a compact Hausdorff space and a filter of dense open subsets of X . A morphism f ( Y , 𝒢 ) ( X , ) is a continuous function f Y X for which f - 1 ( F ) 𝒢 whenever F . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically address only one of these...

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