TeXipedia

xleftharpoondown

Draws a left-pointing harpoon arrow with a downward barb beneath mathematical expressions.

Overview

Primarily used in advanced mathematics and theoretical physics to denote specialized mappings or transformations.

  • Common in category theory for depicting specific morphisms or functors
  • Useful in abstract algebra for representing particular types of operations or maps
  • Often appears in conjunction with other arrow notations to create complex mathematical relationships
  • Particularly valuable when precise arrow directionality and style are needed to convey specific mathematical concepts

Examples

Indicating a downward mapping between sets.

f:X↽ϕYf: X \xleftharpoondown{\phi} Y 
f: X \xleftharpoondown{\phi} Y

Representing a reverse reaction rate in chemical kinetics.

Ratereverse↽k−1k−1[C][D]\text{Rate}_{reverse} \xleftharpoondown{k_{-1}} k_{-1}[C][D] 
\text{Rate}_{reverse} \xleftharpoondown{k_{-1}} k_{-1}[C][D]