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Linking the closure and orthogonality properties of perfect morphisms in a category

David Holgate (1998)

Commentationes Mathematicae Universitatis Carolinae

We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.

Local extension of maps.

Barr, Michael, Kennison, John F., Raphael, R. (2009)

The New York Journal of Mathematics [electronic only]

Natural sinks on Y β

J. Schröder (1992)

Commentationes Mathematicae Universitatis Carolinae

Let ( e β : 𝐐 Y β ) β Ord be the large source of epimorphisms in the category Ury of Urysohn spaces constructed in [2]. A sink ( g β : Y β X ) β Ord is called natural, if g β e β = g β ' e β ' for all β , β ' Ord . In this paper natural sinks are characterized. As a result it is shown that Ury permits no ( E p i , ) -factorization structure for arbitrary (large) sources.

Neighborhood spaces.

Kent, D.C., Min, Won Keun (2002)

International Journal of Mathematics and Mathematical Sciences

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