A function from to is injective if whenever . An injective function is also called one-to-one or an injection; it is the same as a monomorphism in the category of sets.
A bijection is a function that is both injective and surjective.
In constructive mathematics, a strongly extensional function between sets equipped with tight apartness relations is called strongly injective if whenever (which implies that the function is injective). This is the same as a regular monomorphism in the category of such sets and strongly extensional functions (while any merely injective function, if strongly extensional, is still a monomorphism). Some authors use ‘one-to-one’ for an injective function as defined above and reserve ‘injective’ for the stronger notion.