TeXipedia

mapsto

Denotes a mapping or function assignment, indicating that one value is mapped to another in mathematical expressions.

Overview

Essential in mathematical function notation and category theory for explicitly showing how elements are transformed or assigned.

  • Commonly used in set theory to define functions and describe transformations
  • Appears frequently in abstract algebra when defining homomorphisms
  • Helpful in computer science for describing algorithms and transformations
  • Distinguished from regular arrows by emphasizing the assignment nature of the relationship rather than just implication

Examples

Defining a function mapping x to its square.

f:x↦x2f: x \mapsto x^2 
f: x \mapsto x^2

Showing a transformation from real numbers to complex numbers.

R∋x↦eix∈C\mathbb{R} \ni x \mapsto e^{ix} \in \mathbb{C} 
\mathbb{R} \ni x \mapsto e^{ix} \in \mathbb{C}

Describing a linear transformation between vector spaces.

T:V↦WT: V \mapsto W 
T: V \mapsto W