TeXipedia

leftarrowtail

Represents a leftward arrow with a tail, commonly used in mathematical notation to indicate specific mappings or relationships.

Overview

Primarily used in advanced mathematics and theoretical computer science to denote specialized functions or mappings.

  • Often appears in category theory to represent particular types of morphisms
  • Used in abstract algebra for depicting specific mathematical transformations
  • Helpful in formal logic and set theory for expressing precise relationships between elements
  • Frequently combined with other arrow notations to create more complex mathematical statements

Examples

Showing a normal subgroup relationship in group theory.

H↢GH \leftarrowtail G 
H \leftarrowtail G

Indicating a monomorphism (injective homomorphism) between algebraic structures.

Z↢Q\mathbb{Z} \leftarrowtail \mathbb{Q} 
\mathbb{Z} \leftarrowtail \mathbb{Q}

Representing a proper inclusion map between vector spaces.

V1↢V2↢V3V_1 \leftarrowtail V_2 \leftarrowtail V_3 
V_1 \leftarrowtail V_2 \leftarrowtail V_3