nLab arrow

The term arrow is sometimes used as a synonym for morphism, map, and also for directed edge (in a directed graph or quiver).

In computer science it may also refer to a concept generalizing monads, see at arrow (in computer science).

Abbreviations for the class of all arrows of a category $\mathsf{C}$ used in the literature include $\mathrm{Arr}(\mathsf{C})$, $\mathrm{Ar}(\mathsf{C})$, and $\mathrm{Mor}(\mathsf{C})$. Note that this is the class of objects of the arrow category of $\mathsf{C}$, and the same notations are sometimes used for that whole category.

category: disambiguation