| Publication type: |
Article |
| Author: |
Lutz Schröder, Horst Herrlich |
| Title: |
Free factorizations |
| Volume: |
9 |
| Page(s): |
571 – 593 |
| Journal: |
Applied Categorical Structures |
| Year published: |
2001 |
| 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.
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| PostScript Version: |
http://www.informatik.uni-bremen.de/~lschrode/APCS3.ps |
| Keywords: |
factorization retraction graph category word problem |
| Status: |
Reviewed |
| Last updated: |
27. 02. 2004 |
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