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Weak inclusion systems. (English) Zbl 0886.18001
A weak inclusion system in the sense of the authors is nothing but a skeletal version of an $$({\mathfrak E}, {\mathfrak M})$$-factorization system for morphisms in a category, with $${\mathfrak M}$$ a class of monomorphisms. The authors present skeletal counterparts of known properties for the classes $${\mathfrak E}$$ and $${\mathfrak M}$$; see C. M. Ringel [Math. Z. 117, 249-266 (1970; Zbl 0206.30002)], P. J. Freyd and G. M. Kelly [J. Pure Appl. Algebra 2, 169-191 (1972; Zbl 0257.18005)], and for the notions of initiality and finality also O. Wyler [Gen. Topology Appl. 1, 17-28 (1971; Zbl 0215.51502)].

##### MSC:
 18A32 Factorization systems, substructures, quotient structures, congruences, amalgams 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A35 Categories admitting limits (complete categories), functors preserving limits, completions
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