TeXipedia

downharpoonleft

Represents a downward-pointing harpoon with the barb oriented to the left, commonly used in mathematical notation and vector operations.

Overview

Serves as a specialized mathematical arrow notation, particularly useful in advanced mathematics and theoretical physics contexts.

  • Often employed in category theory and abstract algebra to denote specific mappings or transformations
  • Used in conjunction with other harpoon arrows to indicate paired operations or dual relationships
  • Appears in specialized notation systems for describing morphisms and functional relationships
  • Frequently combined with other arrow symbols to create complex mathematical expressions

Examples

Representing a downward left-pointing harpoon vector in a vector field equation.

F(x,y)=xy\vec{F}(x,y) = x\downharpoonleft y
\vec{F}(x,y) = x\downharpoonleft y

Denoting a specialized mapping operation in category theory.

f:ABf: A \downharpoonleft B
f: A \downharpoonleft B

Indicating a specific mathematical relation in order theory.

xy    xyx \downharpoonleft y \iff x \leq y
x \downharpoonleft y \iff x \leq y