Notes on commutation of limits and colimits

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

Notes on commutation of limits and colimits

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

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	527-532
Number of pages	6
Journal	Theory and Applications of Categories
Volume	30
State	Published - Apr 30 2015

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Keywords

Colimit
Fitered colimit
Galois connection
Group action
Limit
Simple group

Cite this

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T1 - Notes on commutation of limits and colimits

AU - Bjerrum, Marie

AU - Johnstone, Peter

AU - Leinster, Tom

AU - Sawin, William F.

N1 - Publisher Copyright: © Marie Bjerrum, Peter Johnstone, Tom Leinster, William F. Sawin, 2014.

PY - 2015/4/30

Y1 - 2015/4/30

N2 - 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.

AB - 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.

KW - Colimit

KW - Fitered colimit

KW - Galois connection

KW - Group action

KW - Limit

KW - Simple group

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SN - 1201-561X

VL - 30

SP - 527

EP - 532

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

ER -

Notes on commutation of limits and colimits

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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