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Amalgamations of Categories

Published online by Cambridge University Press:  20 November 2018

John MacDonald  and
Laura Scull
John MacDonald
Affiliation:
The University of British Columbia, Department of Mathemtics, Vancouver, BC, Canada e-mail: [email protected]
Laura Scull
Affiliation:
Department of Mathematics, Fort Lewis College, Durango, CO 81301, USA e-mail: scull [email protected]
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Abstract

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We consider the pushout of embedding functors in Cat, the category of small categories. We show that if the embedding functors satisfy a 3-for-2 property, then the induced functors to the pushout category are also embeddings. The result follows from the connectedness of certain associated slice categories. The condition is motivated by a similar result for maps of semigroups. We show that our theorem can be applied to groupoids and to inclusions of full subcategories. We also give an example to show that the theorem does not hold when the property only holds for one of the inclusion functors, or when it is weakened to a one-sided condition.

Keywords

18A3018B4020L17categorypushoutamalgamation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 273 - 284
Copyright
Copyright © Canadian Mathematical Society 2009

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