nLab
target

Contents

Definition

The target object, or simply target, of a morphism f:xyf: x \to y in some category CC is the object yy. The target of ff is also called its codomain, since the dual concept (the source) is also called ‘domain’.

Given a small category CC with set of objects C 0C_0 and set of morphisms C 1C_1, the target function of CC is the function t:C 1C 0t: C_1 \to C_0 that maps each morphism in C 1C_1 to its target object in C 0C_0.

Generalising this, given an internal category CC with object of objects C 0C_0 and object of morphisms C 1C_1, the target morphism of CC is the morphism t:C 1C 0t: C_1 \to C_0 that is part of the definition of internal category.

Revised on July 8, 2013 10:24:36 by Urs Schreiber (89.204.135.61)