Advertisement

Preliminaries on Subobjects, Images, and Inverse Images

  • D. Dikranjan
  • W. Tholen
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 346)

Abstract

In this chapter we provide the basic categorical framework on subobjects, inverse images and image factorization as needed throughout the book.

Keywords

Commutative Diagram Inverse Image Closure Operator Natural Transformation Categorical Property 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. Finding an adequate notion of factorization system in a category has been a theme in category theory almost from the very beginnings. Early references include Mac Lane [1948] and Isbell [1957], but it was not before the late sixties to early seventies that a generally accepted definition emerged, most comprehensively presented by Freyd and Kelly [1972], but see also Kennison [1968], Herrlich [1968], Ringel [1970], Pumplün [1972], Dyckhoff [1972] and Bousfield [1977]; it is the self-dual notion of (ε, M) factorization system as presented here in 1.8. We have chosen to take a “one-sided” approach to it via right M- factorizations (going back to Ehrbar and Wyler [1968], [1987], Tholen [1979], [1983] and MacDonald and Tholen [1982]) since idempotent closure operators “are” exactly such factorization systems, as will be made precise in 5.3. The notion of finite M-completeness and its characterization by Theorem 1.6 does not seem to have appeared previously in the literature. Theorem 1.7 goes back to Im and Kelly [1986].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • D. Dikranjan
    • 1
  • W. Tholen
    • 2
  1. 1.Department of MathematicsUniversity of UdineUdineItaly
  2. 2.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

Personalised recommendations