TeXipedia

smile

Represents a curved upward arc symbol commonly used in mathematical relations and abstract algebra.

Overview

Primarily found in advanced mathematics to denote specific binary relations or operations, particularly in abstract algebra and set theory. The curved smile-like shape serves as a visual indicator for certain mathematical relationships.

  • Frequently appears in category theory and abstract algebra notation
  • Used to denote particular types of morphisms or relations between mathematical objects
  • Often employed alongside similar relation symbols like frown in formal mathematical writing

Examples

Expressing a binary relation in set theory or abstract algebra.

A⌣BA \smile B 
A \smile B

Defining a smile operation between elements x and y.

x⌣y=zx \smile y = z 
x \smile y = z

Using the smile relation in a mathematical expression with multiple relations.

P⌣Q  ⟹  R⌣SP \smile Q \implies R \smile S 
P \smile Q \implies R \smile S