Algebraic structures | Homological algebra | K-theory

Grothendieck group

In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed from M in the most universal way, in the sense that any abelian group containing a homomorphic image of M will also contain a homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from a specific case in category theory, introduced by Alexander Grothendieck in his proof of the Grothendieck–Riemann–Roch theorem, which resulted in the development of K-theory. This specific case is the monoid of isomorphism classes of objects of an abelian category, with the direct sum as its operation. (Wikipedia).

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From playlist Mathematics

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From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective

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Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (1/4)

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