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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

UnicodeU+2210
HTML Entity∐
HTML Code∐
CSS\2210

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.

Related symbols