A characterisation of algebraic exactness

Richard Garner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


An algebraically exact category is one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Adámek, Lawvere and Rosický: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conjectured that a complete and sifted-cocomplete category should be algebraically exact just when it is Barr-exact, finite limits commute with filtered colimits, regular epimorphisms are stable by small products, and filtered colimits distribute over small products. We prove this conjecture.

Original languageEnglish
Pages (from-to)1421-1426
Number of pages6
JournalJournal of Pure and Applied Algebra
Issue number8
Publication statusPublished - Aug 2013


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