➕ A math sum 🏭 A joint product

coproduct

9.9

A way in math to join objects into one while keeping their items separate, like putting two sets together

noun
/ˈkoʊprəˌdʌkt/

Specialized

: coproducción

In category theory, the coproduct generalizes the idea of a disjoint union of sets.

Examples

The coproduct of two groups can be thought of as their free product in algebra.
The coproduct of two sets is a fundamental concept in category theory.
Understanding the coproduct helps mathematicians study relationships between different mathematical structures.
In mathematics, a coproduct can be thought of as a disjoint union.
In category theory, the coproduct of two sets is their disjoint union, combining all elements without overlaps.
The mathematical concept of a coproduct is essential for understanding how objects relate in abstract algebra.
When studying functors, you often encounter the coproduct, which serves as a dual concept to the product.

Synonyms

direct sum

vscoproduct

Specialized

8.7

A way of joining two sets or spaces so each new item has one part from each

defines the construction abstractly in category theory as the dual of a product

Surface Forms

coproduct singular

coproducts plural

Morphology

coproduct = product (semi-transparent) = co + product

Formally 'co-' + 'product' is clear, but in category theory 'co-' signals a technical dual notion rather than simple 'together', which may be unfamiliar to general learners.

Etymology

Coproduct comes from the parts co- 'together' and product 'thing made', so it literally means a 'thing made together'. In mathematics the coproduct names a way of joining objects like a 'sum' rather than the usual 'product', so the origin helps you remember it is a kind of joining.