When do completion processes give rise to extensive categories?

Stephen Lack*, E. M. Vitale

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider various (free) completion processes: the exact completion and the regular completion of a category with weak finite limits, the pre-regular completion of a category with finite products and weak finite limits, the exact completion of a regular category, the regular reflection of a pre-regular category, and the filtered-colimit completion of a small category. In each case we give necessary and sufficient conditions for the completion to be extensive; or, in the case of the pre-regular completion, for the completion to satisfy a weakened notion of extensivity which we call pre-extensivity.

Original languageEnglish
Pages (from-to)203-230
Number of pages28
JournalJournal of Pure and Applied Algebra
Volume159
Issue number2-3
DOIs
Publication statusPublished - 24 May 2001
Externally publishedYes

Keywords

  • 18A35
  • 18D99
  • 18E10

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