TeXipedia

twoheadleftarrow

Represents a leftward-pointing double-headed arrow, commonly used to denote surjective mappings or reverse implications in mathematics.

Overview

Essential in advanced mathematical notation, particularly in abstract algebra, category theory, and formal logic where precise relationship visualization is crucial.

  • Frequently used to indicate surjective (onto) functions in set theory and algebra
  • Appears in diagram chasing and commutative diagrams
  • Common in theoretical computer science for representing reverse relationships or dependencies
  • Often employed in mathematical proofs to show backward implications or reverse mappings

Examples

Showing a surjective function mapping from set B to set A.

B↞AB \twoheadleftarrow A 
B \twoheadleftarrow A

Indicating a reverse surjective homomorphism between groups.

G2↞G1G_2 \twoheadleftarrow G_1 
G_2 \twoheadleftarrow G_1

Representing a reverse quotient map in topology.

X/∼↞XX/\sim \twoheadleftarrow X 
X/\sim \twoheadleftarrow X