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Notes on commutation of limits and colimits

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Marie Bjerrum, Peter Johnstone, Tom Leinster, William F. Sawin

We show that there are infinitely many distinct closed classes of colimits (in
the sense of the Galois connection induced by commutation of limits and
colimits in **Set**) which are intermediate between the class of
pseudo-filtered colimits and that of all (small) colimits. On the other hand,
if the corresponding class of limits contains either pullbacks or equalizers,
then the class of colimits is contained in that of pseudo-filtered colimits.

Keywords:
Limit, colimit, filtered colimit, group action, simple group, Galois connection

2010 MSC:
18A30, 18B05, 20J99

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 15, pp 527-532.

Published 2015-04-30.

http://www.tac.mta.ca/tac/volumes/30/15/30-15.pdf

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