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On Sifted Colimits in the Presence of Pullbacks by Chen, Ruiyuan is a scholarly article available to read on EtoBox.

What is On Sifted Colimits in the Presence of Pullbacks about?

We show that in a category with pullbacks, arbitrary sifted colimits may be constructed as filtered colimits of reflexive coequalizers. This implies that "lex sifted colimits", in the sense of Garner--Lack, decompose as Barr-exactness plus filtered colimits commuting with finite limits. We also prove generalizations of these results for $\kappa$-small sifted and filtered colimits, and their interaction with $\lambda$-small limits in place of finite ones, generalizing Garner's characterization of algebraic exactness in the sense of Ad\'amek--Lawvere--Rosick\'y. Along the way, we prove a general result on classes of colimits, showing that the $\kappa$-small restriction of a saturated class of colimits is still "closed under iteration".

Author

Chen, Ruiyuan

Published

2021

Language

EN