Lex colimits

Richard Garner*, Stephen Lack

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of "exactness" conditions relating the finite limits and the specified colimits. Some examples are the notions of regular, Barr-exact, lextensive, coherent, or adhesive category. We introduce a general notion of exactness, of which each of the structures listed above, and others besides, are particular instances. The notion can be understood as a form of cocompleteness "in the lex world"-more precisely, in the 2-category of finitely complete categories and finite-limit-preserving functors.

Original languageEnglish
Pages (from-to)1372-1396
Number of pages25
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - Jun 2012


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