Category theory MOC

Diagonal functor

Let and be categories. The corresponding diagonal functor #m/def/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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