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.
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