Coproduct in LaTeX (\coprod)

Where it is used

Upside-down product sign denoting the coproduct, such as a disjoint union of sets.

Category theory and algebraic topology use \coprod_{i \in I} X_i for the coproduct of a family: disjoint union for sets and spaces, direct sum for abelian groups or modules. It is a large operator like \prod, so limits stack under and over it in display style. Do not confuse it with \amalg, its small binary counterpart for exactly two objects, X \amalg Y. Disjoint unions are also written \bigsqcup, which has a cup-like shape; pick whichever your field uses. The dual construction, the categorical product, uses \prod.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Coproduct: $\coprod$

\[ \coprod_{i \in I} X_i \]
\end{document}

Related symbols

• Big Union\bigcup
• Product\prod_{i=1}^{n}
• Big Union with Index\bigcup_{i=1}^{n}
• Product\prod
• Big Intersection\bigcap
• Summation to Infinity\sum_{n=0}^{\infty}

Frequently asked questions

How do I write Coproduct in LaTeX?

Type \coprod in math mode, for example $\coprod_{i \in I} X_i$. It works in plain LaTeX without loading any package.

Which package do I need for \coprod?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\coprod$ 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).