On sifted colimits and generalized varieties

By J. Adámek, Jirí Rosický. Theory and Applications of Categories, 2001

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Filtered colimits, i.e., colimits which commute with finite limits, have a natural generalization to sifted colimits: these are colimits which commute with finite products in sets. Generalized varieties are defined as free completions of small categories under sifted colimits (analogously to finitely accessible categories which are free completions of small categories under filtered colimits). Among complete categories, generalized varieties are precisely the varieties.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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