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A binary operator representing coproducts or disjoint unions in category theory and algebraic structures.

\coprod image

Examples

Coproduct of sets indexed by natural numbers

∐n∈NXn\coprod_{n \in \mathbb{N}} X_n
\coprod_{n \in \mathbb{N}} X_n

Coproduct in category theory (disjoint union)

A≅∐i=1nAiA \cong \coprod_{i=1}^n A_i
A \cong \coprod_{i=1}^n A_i

Coproduct of modules over a ring R

M⊗(∐i∈INi)≅∐i∈I(M⊗Ni)M \otimes (\coprod_{i \in I} N_i) \cong \coprod_{i \in I} (M \otimes N_i)
M \otimes (\coprod_{i \in I} N_i) \cong \coprod_{i \in I} (M \otimes N_i)