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Encyclopaedia of Mathematics

Part of the book series: Encyclopaedia of Mathematics ((ENMA,volume 2))

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Abstract

Coproduct of a family of objects in a category - A concept describing the (categorical analogues of the) construction of a direct sum of modules or a discrete union (bouquet) of sets in the language of morphisms. Let A i iϵI, be an indexed family of objects in a category M. An object S, together with morphisms σ i : A i →S, is called the coproduct of the family A i iϵI, if for any family of morphisms α i : A i →X, iϵI, there exists a unique morphism α: S→X such that σ i α=α i , iϵI.

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Sobolev, A.I. et al. (1995). C. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3795-7_1

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