TeXipedia

leftharpoonup

Displays a left-pointing harpoon symbol with the barb oriented upward, commonly used in mathematical notation and vector operations.

Overview

Serves as a specialized arrow variant in mathematical expressions, particularly useful in advanced algebra, category theory, and theoretical physics.

  • Often employed to denote specific mappings or transformations
  • Frequently appears in conjunction with other arrow notations to indicate specialized relations
  • Used in advanced mathematical texts to represent particular types of morphisms or operations
  • Pairs naturally with \rightharpoonup for expressing bidirectional or complementary relationships

Examples

Representing a left harpoon arrow in a vector relation

ABA \leftharpoonup B
A \leftharpoonup B

Indicating a one-way mapping or transformation

f:XYf: X \leftharpoonup Y
f: X \leftharpoonup Y

Denoting a specific mathematical operation or action

xy=zx \leftharpoonup y = z
x \leftharpoonup y = z