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Equivalence of Topologically-Algebraic and Semi-Topological Functors

  • H. Herrlich (a1), R. Nakagawa (a2), G. E. Strecker (a3) and T. Titcomb (a3)

Extract

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 .

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References

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1. Börger, R. and Tholen, W., Remarks on topologically algebraic functors, Preprint.
2. Herrlich, H., Initial completions, Math. Z. 150 (1976), 101110.
3. Herrlich, H. and Strecker, G. E., Semi-universal maps and universal initial completions. To appear in Pacific J. Math.
4. Hoffman, R.-E., Semi-identifying lifts and a generalization of the duality theorem for topological functors, Math. Nachr. 74 (1976), 295307.
5. Hoffman, R.-E., Note on semi-topological functors, Math. Z. 160 (1978), 6974.
6. Hong, S. S., Categories in which every mono-source is initial, Kyungpook Math. J. 15 (1975), 133139.
7. Hong, Y. H., Studies on categories of universal topological algebras, Thesis, McMaster University (1974).
8. Hong, Y. H., On initially structured functors, J. Korean Math. Soc. 14 (1978), 159165.
9. Tholen, W., Semi-topological functors I, J. Pure Appl. Alg. 15 (1979), 5373.
10. Trnkovä, V., Automata and categories, Lecture notes in Computer Science 32 (Springer-Verlag, 1975), 132152.
11. Wischnewsky, M. B., A lifting theorem for right adjoints, Cahiers Topologie Géom. Différentielle 19 (1978), 155168.
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Equivalence of Topologically-Algebraic and Semi-Topological Functors

  • H. Herrlich (a1), R. Nakagawa (a2), G. E. Strecker (a3) and T. Titcomb (a3)

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