TeXipedia

twoheadrightarrow

Represents a surjective (onto) function mapping between mathematical sets or structures.

Overview

Essential in advanced mathematics for depicting surjective mappings where every element in the codomain has at least one corresponding element in the domain.

  • Commonly used in abstract algebra and category theory to show onto mappings
  • Appears frequently in group theory and homomorphism discussions
  • Helps distinguish surjective functions from general functions or other types of mappings
  • Often paired with other arrow symbols to illustrate different types of mathematical relationships

Examples

Showing a surjective (onto) function mapping between sets.

f:X↠Yf: X \twoheadrightarrow Y 
f: X \twoheadrightarrow Y

Indicating a surjective group homomorphism in abstract algebra.

ϕ:G↠H\phi: G \twoheadrightarrow H 
\phi: G \twoheadrightarrow H

Representing a quotient map in topology.

π:E↠E/∼\pi: E \twoheadrightarrow E/\sim 
\pi: E \twoheadrightarrow E/\sim