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Preliminaries

  • Güter Tamme
Part of the Universitext book series (UTX)

Abstract

Let C be a category and let u : AB be a morphism in C. Then u is called a monomorphism (or injective) if the map Hom(C, A) → Hom(C,B) which sends v to uv is injective for all objects C in C. Analogously, u is called an epimorphism (or surjective) if the map Hom(B, C) → Hom(A, C) which sends w to wu is injective for all CC. The morphism u is bijective if u is both injective and surjeetive. An isomorphism, i.e. a morphism having an inverse, is always bijective. The converse is not true in general.

Keywords

Exact Sequence Spectral Sequence Short Exact Sequence Natural Transformation Inductive Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Güter Tamme
    • 1
  1. 1.Mathematisches InstitutUniversität RegensburgRegensburgGermany

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