1morphism

1morphism is a concept primarily found in category theory, a branch of abstract mathematics. In essence, a 1morphism represents a "morphism" or "arrow" between objects within a category. A category is defined by a collection of objects and a collection of morphisms, where each morphism has a source object and a target object. The 1morphism is the fundamental building block of such a category. It signifies a relationship or transformation from one object to another.

For example, in the category of sets, the objects are sets, and the 1morphisms are functions between these sets. If A and B are sets, a function f: A -> B is a 1morphism from object A to object B. In the category of vector spaces, objects are vector spaces, and 1morphisms are linear transformations between them. The composition of 1morphisms is also a key property of categories. If there is a 1morphism f from object A to object B, and another 1morphism g from object B to object C, then their composition, denoted as g o f, is a 1morphism from object A to object C. This composition must satisfy associativity. Identity 1morphisms also exist for each object, acting as neutral elements for composition. The term "1morphism" distinguishes these basic arrows from higher-order morphisms that may exist in higher categories.