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On sifted colimits and generalized varieties

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J. Adamek and J. Rosicky

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.

Keywords:

2000 MSC:

*Theory and Applications of Categories*, Vol. 8, 2001, No. 3, pp 33-53.

http://www.tac.mta.ca/tac/volumes/8/n3/n3.dvi

http://www.tac.mta.ca/tac/volumes/8/n3/n3.ps

http://www.tac.mta.ca/tac/volumes/8/n3/n3.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n3/n3.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n3/n3.ps

Revised 2007-01-22. Original version at

http://www.tac.mta.ca/tac/volumes/8/n3/n3a.dvi

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