TeXipedia

xhookleftarrow

Produces an extensible left-pointing hooked arrow that automatically adjusts its width based on the subscript or superscript content.

Overview

Serves as a specialized arrow notation commonly used in advanced mathematics and category theory to denote specific types of mappings or relationships.

  • Particularly useful when the text above or below the arrow is long, as the arrow automatically stretches to accommodate it
  • Often employed in commutative diagrams and algebraic notation
  • Provides a more sophisticated alternative to standard arrows when indicating special morphisms or mappings
  • Frequently appears in advanced algebra, homological algebra, and theoretical computer science documentation

Examples

Showing a mapping with a condition above a hooked left arrow.

X↩n→∞YX \xhookleftarrow{n \to \infty} Y 
X \xhookleftarrow{n \to \infty} Y

Indicating an inverse relationship with additional notation.

f−1(B)↩subsetBf^{-1}(B) \xhookleftarrow{\text{subset}} B 
f^{-1}(B) \xhookleftarrow{\text{subset}} B

Representing a pullback in category theory.

F(A)↩ϕAF(A) \xhookleftarrow{\phi} A 
F(A) \xhookleftarrow{\phi} A