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morphism [ˈmɔːfɪzəm] N

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The existence of this morphism is a consequence of the universal property which characterizes the product (up to isomorphism). en.wikipedia.org

The identity morphism (identity mapping) is called the trivial automorphism in some contexts. en.wikipedia.org

Note that the domain and codomain are in fact part of the information determining a morphism. en.wikipedia.org

A split epimorphism is a morphism which has a right-sided inverse. en.wikipedia.org

There are two operations which are defined on every morphism, the domain (or source) and the codomain (or target). en.wikipedia.org

This morphism is birational for of dimension at most 2. en.wikipedia.org

If a category has zero morphisms, then one can define the notions of kernel and cokernel for any morphism in that category. en.wikipedia.org

The product of some objects has a canonical projection morphism to each factor. en.wikipedia.org

Both the object set and the morphism set are sets, so it becomes possible to discuss the category of all sets without invoking proper classes. en.wikipedia.org

This may be extended by induction to a canonical morphism from any finite coproduct to the corresponding product. en.wikipedia.org

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