Equivalence of categories

This article defines a functor property: a property that can be evaluated to true/false given a functor between two categories.
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Definition

Symbol-free definition

An equivalence of categories is a functor between two categories that satisfies the following three conditions:

• It is full: It is surjective on the collection of morphisms between any two objects.
• It is faithful: It is injective on the collection of morphisms between any two objects.
• it is essentially surjective: Every object in the target category is isomorphic to the image under the functor of some object in the source category.