Geodesic
Equivalence of Topologically-Algebraic and Semi-Topological Functors
Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 34-39

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Throughout let be faithful.1.1. A U-morphism with domain X is a pair (e, A), where e ∈ Hom (X, UA). A [U-morphism (e, A) is called U-epi ( = generating) provided that r, s ∈ Hom (A, A’) and (Ur)e = (Us)e imply that r = s.1.2. A U-source is a pair (X, (fi,Ai)I), (written more simply (X, (fi,Ai)I),, where (fi,Ai)I 7 is a family of U-morphisms each with domain X.1.3. A factorization of a U-source (X,fi,Ai)I is a triple (e,A,gi)I such that (e, A) is a U-morphisms with domain X and for each i ∈ I gi ∈ Hom (A,Ai) and (Ug i )e = f i . 
Herrlich, H.; Nakagawa, R.; Strecker, G. E.; Titcomb, T. Equivalence of Topologically-Algebraic and Semi-Topological Functors. Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 34-39. doi: 10.4153/CJM-1980-004-x
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