Homology, Homotopy and Applications
Volume 17 (2015)
Algebraic proofs of some fundamental theorems in algebraic $K$-theory
Pages: 267 – 280
We present new proofs of the additivity, resolution, and cofinality theorems for the algebraic $K$-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic $K$-groups via binary complexes.
higher algebraic $K$-group, acyclic binary complex, additivity theorem, resolution theorem, cofinality theorem
2010 Mathematics Subject Classification