TeXipedia

longmapsto

Represents a long right arrow with a vertical bar at the start, commonly used to denote function mappings or transformations in mathematics.

Overview

Serves as a more visually prominent alternative to the standard mapsto arrow, particularly useful in mathematical contexts where mappings need to be emphasized.

  • Frequently used in abstract algebra and category theory to show explicit function definitions
  • Common in commutative diagrams and mathematical proofs
  • Helpful for displaying transformations between sets or spaces
  • Often appears in textbooks and academic papers when defining functions or showing mathematical correspondences

Examples

Function mapping notation in category theory showing a morphism between objects.

X⟼YX \longmapsto Y 
X \longmapsto Y

Explicit function definition showing variable transformation.

x⟼x2+2x+1x \longmapsto x^2 + 2x + 1 
x \longmapsto x^2 + 2x + 1

Set mapping notation showing element correspondence.

a∈A⟼f(a)∈Ba \in A \longmapsto f(a) \in B 
a \in A \longmapsto f(a) \in B