Initial and terminal objects
Special objects used in (mathematical) category theory / From Wikipedia, the free encyclopedia
"Zero object" redirects here. For zero object in an algebraic structure, see zero object (algebra).
"Terminal element" redirects here. For the project management concept, see work breakdown structure.
In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X.
The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
If an object is both initial and terminal, it is called a zero object or null object. A pointed category is one with a zero object.
A strict initial object I is one for which every morphism into I is an isomorphism.