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Monomorphisms, Epimorphisms, and Pull-Backs

  • G. M. Kelly (a1)
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As the applications of category theory increase, we find ourselves wanting to imitate in general categories much that was at first done only in abelian categories. In particular it becomes necessary to deal with epimorphisms and monomorphisms, with various canonical factorizations of arbitrary morphisms, and with the relations of these things to such limit operations as equalizers and pull-backs.

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References
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[1]Bourbaki, N., Eléments de mathématique: Livre III (Topologie générale) (Ch. I, 3me Éd. Paris, 1961).
[2]Grothendieck, A., ‘Technique de descente et théorèmes d'existence en géométrie algébrique. I’, Séminaire Bourbaki 12 (1959/1960), Exp. 190.
[3]Grothendieck, A., ‘Techniques de construction et théorémes d'existence en géométrie algébrique. III’, Séminaire Bourbaki 13 (1960/1961), Exp. 212.
[4]Isbell, J. R., ‘Subobjects, adequacy, completeness and categories of algebras’, Rozprawy Mat. 36 (1964) 132.
[5]Isbell, J. R., ‘Structure of categories’, Bull. Amer. Math. Soc. 72 (1966), 619November655.
[6]Oort, F., ‘On the definition of an abelian category’, Nederl. Akad. Wetensch. Proc. Ser. A 70 (Indag. Math. 29) (1967), 8392.
[7]Pupier, R., ‘Sur les décompositions de morphismes dans les catégories à sommes ou à produits fibrés’, C. R. Acad. Sci. Paris 258 (1964), 63176319.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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