injektiva

Injektiva is a term used in mathematics, specifically in the field of set theory and category theory. It refers to a function or a morphism that is both injective and surjective. In other words, an injektiva function is one that is one-to-one and onto.

In the context of set theory, an injektiva function f: A → B is a function that maps each element of set A to a unique element of set B, and every element of B is the image of some element of A. This means that f is both injective (one-to-one) and surjective (onto).

In category theory, the concept of injektiva is generalized to morphisms in any category. A morphism f: A → B is said to be injektiva if it is both monic (injective) and epic (surjective). This means that f is both left-cancellable and right-cancellable, i.e., for any morphisms g and h, if f ∘ g = f ∘ h, then g = h, and if g ∘ f = h ∘ f, then g = h.

Injektiva functions and morphisms play an important role in various areas of mathematics, including algebra, topology, and logic. They are used to study the structure of mathematical objects and to establish relationships between different mathematical concepts.