Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T08:06:29.620Z Has data issue: false hasContentIssue false
  • English
  • Français

Monomorphisms, Epimorphisms, and Pull-Backs

Published online by Cambridge University Press:  09 April 2009

G. M. Kelly
G. M. Kelly
Affiliation:
The University of New South Wales
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 124 - 142
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Bourbaki, N., Eléments de mathématique: Livre III (Topologie générale) (Ch. I, 3me Éd. Paris, 1961).Google Scholar
[2]Grothendieck, A., ‘Technique de descente et théorèmes d'existence en géométrie algébrique. I’, Séminaire Bourbaki 12 (1959/1960), Exp. 190.Google Scholar
[3]Grothendieck, A., ‘Techniques de construction et théorémes d'existence en géométrie algébrique. III’, Séminaire Bourbaki 13 (1960/1961), Exp. 212.Google Scholar
[4]Isbell, J. R., ‘Subobjects, adequacy, completeness and categories of algebras’, Rozprawy Mat. 36 (1964) 1–32.Google Scholar
[5]Isbell, J. R., ‘Structure of categories’, Bull. Amer. Math. Soc. 72 (1966), 619November–655.CrossRefGoogle Scholar
[6]Oort, F., ‘On the definition of an abelian category’, Nederl. Akad. Wetensch. Proc. Ser. A 70 (Indag. Math. 29) (1967), 83–92.CrossRefGoogle Scholar
[7]Pupier, R., ‘Sur les décompositions de morphismes dans les catégories à sommes ou à produits fibrés’, C. R. Acad. Sci. Paris 258 (1964), 6317–6319.Google Scholar