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Amalgamations of Categories

  Published:2009-06-01
 Printed: Jun 2009
  • John MacDonald
  • Laura Scull
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Abstract

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: category, pushout, amalgamation category, pushout, amalgamation
MSC Classifications: 18A30, 18B40, 20L17 show english descriptions Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
unknown classification 20L17
18A30 - Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
20L17 - unknown classification 20L17
 

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