hookrightarrow
Represents an injective (one-to-one) mapping or embedding between mathematical structures.
Overview
Commonly used in advanced mathematics to denote special types of functions or morphisms that preserve structure while mapping elements uniquely.
- Essential in category theory for depicting faithful functors and embeddings
- Appears frequently in algebra to show subgroup or subspace inclusions
- Used in topology to indicate embedding of one space into another
- Helpful in set theory for showing injective relationships between sets
Examples
Showing an injective function mapping from set A to B.
f: A \hookrightarrow BIndicating a subset embedding into a larger space.
\mathbb{N} \hookrightarrow \mathbb{Z} \hookrightarrow \mathbb{Q}Denoting the canonical inclusion of a subgroup.
H \hookrightarrow G