Categorical product

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Definition

Suppose is a category and . A categorical product, or simply product, of and is an object along with morphisms (called projection maps) , such that the following holds:

For any object and morphisms , there is a unique morphism such that and .

If a categorical product exists for two objects, then the categorical product is unique upto canonical isomorphism: for any two categorical products, there is a unique isomorphism between them that commutes with the projection maps.