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looparrowleft

Displays a curved arrow that loops counterclockwise, commonly used in mathematical diagrams and mappings.

Overview

Serves as a specialized mathematical arrow notation primarily used to indicate recursive operations, self-referential mappings, or cyclic processes in advanced mathematics and theoretical computer science.

  • Frequently appears in category theory to denote endomorphisms
  • Used in abstract algebra for depicting cyclic group operations
  • Helpful in algorithmic flowcharts to show loop structures or recursive procedures
  • Common in mathematical logic for representing fixed-point operations

Examples

Showing a cyclic process or operation that loops leftward.

f(x)↫g(x)f(x) \looparrowleft g(x) 
f(x) \looparrowleft g(x)

Indicating a leftward recursive relationship in a sequence.

xn+1↫xnx_{n+1} \looparrowleft x_n 
x_{n+1} \looparrowleft x_n

Representing a left-rotating transformation or mapping.

T:V↫VT: V \looparrowleft V 
T: V \looparrowleft V