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Elementary observations on 2-categorical limits

Published online by Cambridge University Press:  17 April 2009

G.M. Kelly
G.M. Kelly
Affiliation:
Pure Mathematics DepartmentUniversity of SydneyN.S.W. 2006Australia
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Abstract

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With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 2 , April 1989 , pp. 301 - 317
Copyright
Copyright © Australian Mathematical Society 1989

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