unitpreservation
Unit preservation, sometimes written as unit-preservation, is the property of a map, morphism, or functor to preserve the identity element (the unit) of a given algebraic or categorical structure. In many areas, preserving the unit is part of preserving the overall structure.
In algebra, a ring homomorphism φ: R → S that satisfies φ(1_R) = 1_S is called unital or unit-preserving;
In category theory, for monoidal categories, a functor F is strong monoidal if it comes equipped with
In other algebraic contexts, a homomorphism is often required to preserve designated constants or units, and
See also: unit element, unital homomorphism, strong monoidal functor, monoidal category.