On sifted colimits and generalized varieties

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Authors	ADÁMEK J. ROSICKÝ J.
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Theory and Applications of Categories
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	sifted colimit;variety
Description	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.
Related projects:	Categorical methods of the theory of structures and computer science Mathematical structures of algebra and geometry