In mathematics, the Yoneda lemma is a fundamental result in category theory. It is an abstract result on functors of the type morphisms into a fixed object...

Tokyo in 1990, he moved to Tokyo Denki University. The Yoneda lemma in category theory and the Yoneda product in homological algebra are named after him....

are completely known and easy to describe; this is the content of the Yoneda lemma. Saunders Mac Lane, one of the founders of category theory, is said to...

groupoids. Showing this 2-functor is a sheaf is the content of the 2-Yoneda lemma. Using the Grothendieck construction, there is an associated category...

rise to a natural transformation Hom(–, f) : Hom(–, B) → Hom(–, B′) Yoneda's lemma implies that every natural transformation between Hom functors is of...

Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma Zorn's lemma While these...

can be addressed for the graph example and related examples via the Yoneda Lemma as described in the Further examples section below, but this then ceases...

{\displaystyle C} in a functor category that was mentioned earlier uses the Yoneda lemma as its main tool. For every object X {\displaystyle X} of C {\displaystyle...

M)(U_{i})=\operatorname {Hom} (yU_{i},{\mathcal {H}}om(\eta ,M))} by the Yoneda lemma, we have: Hom D ⁡ ( η ~ F , M ) = Hom D ⁡ ( lim → ⁡ η U i , M ) = lim...

categories Subcategory Faithful functor Full functor Forgetful functor Yoneda lemma Representable functor Functor category Adjoint functors Galois connection...