nLab
cartesian object

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2-category theory

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A cartesian object in a 2-category with finite limits is an object A such that the diagonal morphism A→A×A and the unique map A→1 have right adjoints. Any cartesian object is automatically a pseudomonoid in a canonical way.

For example, a cartesian object in Cat is precisely a category with finite products, which is of course a monoidal category in a canonical way.

Revised on May 21, 2010 19:15:48 by Mike Shulman (128.192.37.11)
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