N-ary Coproduct Symbol
∐ denotes an N-ary coproduct, commonly used in category theory and related math notation.
U+2210
The symbol ∐ represents an N-ary coproduct. It’s used to express a general “sum-like” construction indexed by multiple objects. Below you’ll find practical ways to copy it and understand how it’s used.
N-ary Coproduct Symbol Meaning
∐ (U+2210) is the “N-ary coproduct” symbol. In category theory, it denotes a coproduct over N (or more generally a family indexed by a set) of objects. Conceptually, it behaves like an abstract alternative to addition: instead of combining inputs into a product, a coproduct combines them by providing canonical injections into a universal object. In many contexts, it corresponds to constructions such as disjoint unions or direct sums, depending on the category you’re working in. Use ∐ when the problem calls for a universal “co-sum” style assembly across multiple components.
Common uses
- •Writing category theory expressions that define a universal coproduct for multiple objects
- •Denoting disjoint unions (in settings where coproducts correspond to them)
- •Formulating proofs that involve injections into a coproduct object
- •Labeling components in algebraic or type-theory diagrams that model coproduct structure
- •Documenting notation in math notes, lecture slides, or technical blog posts
Examples
∐ N-ary Coproduct Symbol (U+2210)
- ∐Let ∐_{i=1}^N A_i be the coproduct of objects A_1 through A_N.
- ∐There exist canonical injections A_i → ∐ A_i for each index i.
- ∐A morphism from ∐ A_i is determined by its components on each A_i.
- ∐In this category, the coproduct corresponds to a disjoint union.
- ∐We define B as the coproduct of C and D, written B = ∐(C, D).
Variations
Ready to copy
Technical codes
| Unicode | U+2210 | |
| HTML Entity | ∐ | |
| HTML Code | ∐ | |
| CSS | \2210 | |
| Alt Code | Alt + 8720 | |
| Decimal | 8720 |
How to type N-ary Coproduct Symbol (∐)
On Windows
Hold Alt and type 8720 on the numeric keypad. In Word, type 2210 then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 2210. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 2210, then press Enter or Space.
Anywhere
Copy ∐ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What is the Unicode code point for ∐?
The symbol ∐ is Unicode code point U+2210.
How do I type ∐ using HTML?
Use the HTML entity ∐.
What does “N-ary coproduct” mean?
It refers to a coproduct construction involving N objects (or more generally a family of objects indexed for the construction).
Is ∐ the same as a summation symbol like ∑?
Not exactly. ∐ denotes coproduct structure in category theory, which is “sum-like” in some contexts but has its own universal-property meaning.