Let be the category whose objects are all commutative K-algebras with identity and whose morphisms are

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Let ℓ  be the category whose objects are all commutative K-algebras with identity and whose morphisms are all K-algebra homomorphisms ∫: A → B such that ∫(1A) = 1B. Then any two K-algebras A, B of ℓ  have a coproduct.

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