When do completion processes give rise to extensive categories?

Stephen Lack*, E. M. Vitale

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Issue number2-3
Publication statusPublished - 24 May 2001
Externally publishedYes


  • 18A35
  • 18D99
  • 18E10


Dive into the research topics of 'When do completion processes give rise to extensive categories?'. Together they form a unique fingerprint.

Cite this