nLab partial functor

Idea

A partial functor is a span $A \leftarrow X \to B$ of functors whose left leg is the inclusion of a cosieve.

These compose by strict pullback and the identity partial functor is given by $A = A = A$. Thereby partial functors form a subbicategory of that of profunctors.

Related concepts

• partial function

References

• Jean Bénabou (notes by Thomas Streicher), Distributors at Work, lectures given at TU Darmstadt (2000) [pdf, pdf]