
Recent Posts
Archives
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: yoneda lemma
Commutative Algebra 29
Distributivity Finally, tensor product is distributive over arbitrary direct sums. Proposition 1. Given any family of modules , we have: Proof Take the map which takes . Note that this is welldefined: since only finitely many are nonzero, only finitely … Continue reading
Posted in Advanced Algebra
Tagged hom functor, induced modules, localization, rightexact, tensor products, yoneda lemma
2 Comments
Commutative Algebra 20
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 rightcomposing with f. Proof Let be a morphism in . We need … Continue reading
Posted in Advanced Algebra
Tagged category theory, coproducts, functors, hom functor, natural transformations, products, yoneda lemma
4 Comments
Commutative Algebra 19
Natural Transformations “I didn’t invent categories to study functors; I invented them to study natural transformations.” – Saunders Mac Lane, one of the founders of category theory A natural transformation is, loosely speaking, a homomorphism between functors. Its definition may … Continue reading