A characterisation of algebraic exactness
نویسنده
چکیده
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 justwhen it is Barr-exact, finite limits commutewith filtered colimits, regular epimorphisms are stable by small products, and filtered colimits distribute over small products. We prove this conjecture. © 2012 Elsevier B.V. All rights reserved.
منابع مشابه
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