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Amalgamations of Categories |
Published:2009-06-01
Printed: Jun 2009
Printed: Jun 2009
- John MacDonald
- Laura Scull
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 |
| MSC Classifications: |
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 |