Cohomology of products and coproducts of augmented algebras

الأصل · EN

We show that the ordinary cohomology functor from the category of augmented k-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are self-injective. We identify the multiplicative structure of the Hochschild cohomology of a product modulo a certain ideal in terms of the cohomology of the factors.