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

Princeton University

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

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

ASJC Scopus subject areas

Mathematics (miscellaneous)

Keywords

Colimit
Fitered colimit
Galois connection
Group action
Limit
Simple group

Cite this

@article{3338dcd6b57343dfbdc366abe413f032,

title = "Notes on commutation of limits and colimits",

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.",

keywords = "Colimit, Fitered colimit, Galois connection, Group action, Limit, Simple group",

author = "Marie Bjerrum and Peter Johnstone and Tom Leinster and Sawin, \{William F.\}",

note = "Publisher Copyright: {\textcopyright} Marie Bjerrum, Peter Johnstone, Tom Leinster, William F. Sawin, 2014.",

year = "2015",

month = apr,

day = "30",

language = "American English",

volume = "30",

pages = "527--532",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

}

TY - JOUR

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

UR - https://www.scopus.com/pages/publications/84979710720

UR - https://www.scopus.com/pages/publications/84979710720#tab=citedBy

M3 - Article

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

ASJC Scopus subject areas

Keywords

Other files and links

Fingerprint

Cite this