TeXipedia

xtwoheadleftarrow

Represents a double-headed leftward arrow with text underneath, commonly used in mathematical notation to indicate specialized mappings or relationships.

Overview

Provides an extended variant of the double-headed left arrow that automatically adjusts its length based on the content placed below it. This symbol is particularly valuable in advanced mathematics and theoretical computer science.

  • Frequently used in category theory to denote specific types of morphisms
  • Common in abstract algebra for indicating specialized homomorphisms or mappings
  • Useful when describing reverse transformations or inverse relationships that require additional notation
  • Often appears in commutative diagrams and formal mathematical proofs where detailed arrow annotations are needed

Examples

Showing a double surjective mapping between sets with a label.

X↞ϕYX \xtwoheadleftarrow{\phi} Y 
X \xtwoheadleftarrow{\phi} Y

Indicating a reverse double surjective homomorphism in group theory.

G↞ψHG \xtwoheadleftarrow{\psi} H 
G \xtwoheadleftarrow{\psi} H

Representing a double surjective pullback in category theory.

A↞f∘gBA \xtwoheadleftarrow{f \circ g} B 
A \xtwoheadleftarrow{f \circ g} B