Tag Archives: coproducts

Commutative Algebra 49

Posted on May 7, 2020 by limsup

Morphism of Diagrams Throughout this article denotes a category and J is an index category. Definition Given diagrams , a morphism is a natural transformation . Thus we have the category of all diagrams in of type J, which we … Continue reading →

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Commutative Algebra 48

Posted on May 6, 2020 by limsup

Introduction For the next few articles we are back to discussing category theory to develop even more concepts. First we will look at limits and colimits, which greatly generalize the concept of products and coproducts and cover loads of interesting … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , , | 4 Comments

Commutative Algebra 30

Posted on April 17, 2020 by limsup

Tensor Product of A-Algebras Proposition 1. Let B, C be A-algebras. Their tensor product has a natural structure of an A-algebra which satisfies . Proof Fix . The map is A-bilinear so it induces an A-linear map Now varying (b, c) gives … Continue reading →

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Commutative Algebra 20

Posted on April 7, 2020 by limsup

Yoneda Lemma For an object , define the covariant functor Proposition 1. Any morphism in gives us a natural transformation In summary, the natural transformation is obtained by right-composing with f. Proof Let be a morphism in . We need … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , , | 4 Comments