Geodesic
On sifted colimits and generalized varieties
Theory and applications of categories, Tome 8 (2001), pp. 33-53.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Filtered colimits, i.e., colimits over schemes $\cal D$ such that $\cal D$-colimits in $\Set$ commute with finite limits, have a natural generalization to sifted colimits: these are colimits over schemes $\cal D$ such that $\cal D$-colimits in $\Set$ commute with finite products. An important example: reflexive coequalizers are sifted colimits. Generalized varieties are defined as free completions of small categories under sifted-colimits (analogously to finitely accessible categories which are free filtered-colimit completions of small categories). Among complete categories, generalized varieties are precisely the varieties. Further examples: category of fields, category of linearly ordered sets, category of nonempty sets.
Classification :
Keywords: 
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     author = {J. Adamek and J. Rosicky},
     title = {On sifted colimits and generalized varieties},
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     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a2/}
}
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J. Adamek; J. Rosicky. On sifted colimits and generalized varieties. Theory and applications of categories, Tome 8 (2001), pp. 33-53. http://geodesic.mathdoc.fr/item/TAC_2001_8_a2/