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Tag Archives: natural transformations
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
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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