Free Factorizations

Authors: Schröder L.; Herrlich H.

Source: Applied Categorical Structures, Volume 9, Number 6, November 2001 , pp. 571-593(23)

Publisher: Springer

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Abstract:

Given any morphism, we construct extensions of the original category in which this morphism admits certain factorizations, in particular a (retraction, section)-factorization. To this end, we solve the word problem for a certain type of systems of generators and relations for categories. This also enables us to prove preservation properties for the said extensions, e.g. preservation of a pair of diagonalizing classes of epimorphisms and monomorphisms.

Iterating such extension processes, we obtain factorizable extensions of categories; in particular, we construct a free proper factorization structure on a given category, which leads to a characterization of preimages of proper factorization structures under full embeddings. As a further application, we characterize an absoluteness property regarding factorizations of functorial images of a morphism.

Keywords: factorization; retraction; graph; category; word problem

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Mathematics, University of Bremen, Pf. 330440, 28334 Bremen, Germany

Publication date: 2001-11-01