Category theory MOC

Diagonal functor

Let and be categories. The corresponding diagonal functor cat

is the functor into the functor category sending each object to the constant functor and each morphism to the natural transformation whose components are all .

In the case , we have , giving the typical binary diagonal functor.

Properties

• The adjoints, if they exist, are limits and colimits of shape in — See Limits and colimits as adjoints to the diagonal

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