TeXipedia

hookleftarrow

Displays a left-pointing arrow with a hook at its tail, commonly used to indicate mappings, returns, or special relations in mathematics.

Overview

Serves as a specialized arrow notation frequently encountered in advanced mathematics and theoretical computer science, particularly when denoting specific types of mappings or relationships.

  • Often used in category theory to represent certain morphisms or functors
  • Appears in programming language theory and lambda calculus notation
  • Useful for indicating return values or reverse mappings in mathematical proofs
  • Common in abstract algebra when describing particular types of homomorphisms

Examples

Indicating a return value or output in a mathematical function definition.

f(x)↩x2f(x) \hookleftarrow x^2 
f(x) \hookleftarrow x^2

Showing a mapping or transformation between sets.

A↩BA \hookleftarrow B 
A \hookleftarrow B

Denoting a return statement in algorithmic pseudocode.

max(x,y)↩{xif x≥yyotherwise\text{max}(x,y) \hookleftarrow \begin{cases} x & \text{if } x \geq y \\ y & \text{otherwise} \end{cases} 
\text{max}(x,y) \hookleftarrow \begin{cases} x & \text{if } x \geq y \\ y & \text{otherwise} \end{cases}