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....

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...

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...

local lemma Nakayama's lemma Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma...

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

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...

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...

D and as morphisms the natural transformations of such functors. The Yoneda lemma is one of the most famous basic results of category theory; it describes...

the homset is understood to be in the opposite category Δop.) By the Yoneda lemma, the n-simplices of a simplicial set X stand in 1–1 correspondence with...