Diagonal functor

In category theory, a branch of mathematics, the diagonal functor $\mathcal{C} \rightarrow \mathcal{C} \times \mathcal{C}$ is given by $\Delta(a) = \langle a,a \rangle$ , which maps objects as well as morphisms. This functor can be employed to give a succinct alternate description of the product of objects within the category $\mathcal{C}$ : a product $a \times b$ is a universal arrow from $\Delta$ to $\langle a,b \rangle$ . The arrow comprises the projection maps.

单词	Diagonal functor
释义	Diagonal functor 英语百科 Diagonal functor In category theory, a branch of mathematics, the diagonal functor $\mathcal{C} \rightarrow \mathcal{C} \times \mathcal{C}$ is given by $\Delta(a) = \langle a,a \rangle$ , which maps objects as well as morphisms. This functor can be employed to give a succinct alternate description of the product of objects within the category $\mathcal{C}$ : a product $a \times b$ is a universal arrow from $\Delta$ to $\langle a,b \rangle$ . The arrow comprises the projection maps.
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