Condensed Learning Seminar

Define the Grothendieck group of a commutative ring. Then define K1 and K2 and 
state Matsumoto’s theorem. Explain the definitions of higher K-theory in terms of the 
+-construction and in terms of the∞-group completion of groupoid of finite projective modules. Define K0 of a stable ∞-category and sketch the Quillen Q-construction and the Waldhausen S-construction. State the Gillet–Waldhausen resolution theorem for the K-theory of rings. Finally, explain the characterization of K-theory as the universal additive invariant of stable ∞-categories.