Hook Right Arrow in LaTeX (\hookrightarrow)

Where it is used

Draws a right arrow with a hooked tail, the standard symbol for an injective map, inclusion, or embedding.

Writing \iota : A \hookrightarrow X tells the reader that the map is an inclusion or injection, without saying so in words. Analysis uses it for continuous embeddings of function spaces, as in H^1(\Omega) \hookrightarrow L^2(\Omega), and compact embeddings are sometimes marked with a further decoration. Category theory uses it for monomorphisms. The surjective counterpart is \twoheadrightarrow. The hook makes the arrow longer than \to, so check alignment in diagrams. It is a relation, so TeX surrounds it with thick spacing.

Also listed under: Functions & Mapping

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Hook Right Arrow: $\hookrightarrow$

\[ H^1(\Omega) \hookrightarrow L^2(\Omega) \]
\end{document}

Related symbols

• Southeast Arrow\searrow
• Hook Left Arrow\hookleftarrow
• Left Harpoon Up\leftharpoonup
• Northeast Arrow\nearrow
• Right Harpoon Up\rightharpoonup
• Long Maps To\longmapsto

Frequently asked questions

How do I write Hook Right Arrow in LaTeX?

Type \hookrightarrow in math mode, for example $H^1(\Omega) \hookrightarrow L^2(\Omega)$. It works in plain LaTeX without loading any package.

Which package do I need for \hookrightarrow?

None. \hookrightarrow is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \hookrightarrow in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\hookrightarrow$ in running text. If you only need the glyph in text, paste the Unicode character ↪ instead (with XeLaTeX or LuaLaTeX and a font that has it).