Aim to give a complete overview of various definitions of K-theory.
(Have not bothered to provide links to the CT pages)
B-theory Algebraic K-theory K-theory Abstract K-theory Hermitian K-theory Milnor K-theory Additive K-theory Equivariant K-theory Etale K-theory Topological K-theory Twisted K-theory Bi-relative algebraic K-theory Bounded K-theory Differential K-theory Homotopy K-theory Infinitesimal K-theory K-theory of categories Multiplicative K-theory Negative K-theory Quillen K-theory Semi-topological K-theory Stable K-theory Algebraic K-theory with compact supports Bousfield’s united K-theory Complex K-theory Controlled algebraic K-theory Equivariant KK-theory Homotopy invariant K-theory K-theory of stacks K-theory with supports KK-theory Motivic cohomology Multirelative K-theory Nonconnected K-theory Real K-theory Reduced K-theory Relative K-theory Smooth K-theory Twisted equivariant K-theory Waldhausen K-theory p-adic K-theory Algebraic K-theory of C-algebras Algebraic Morava K-theory Arithmetic K-theory Compact K-theory Connective topological K-theory Continuously controlled K-theory Controlled K-theory Derivator K-theory Equivariant algebraic K-theory Etale K-theory of ring spectra Holomorphic K-theory K-theory of functors K-theory with coefficients Karoubi-Villamayor K-theory Kasparov’s bivariant K-theory Polyhedral K-theory Quaternionic K-theory Relative algebraic K-theory Self-conjugate K-theory Thomason-Trobaugh K-theory Volodin K-theory l-adic algebraic K-theory Higher arithmetic K-theory K-theory of C-algebras Morava K-theory Nisnevich K-theory Bivariant K-theory Dominant K-theory Secondary K-theory G-theory K-cohomology Algebraic K-homology K-homology KR-theory KT-theory Semi-topological K-homology Algebraic G-theory G-theory of algebraic stacks K’-theory Topological G-theory
nLab page on K10 K-theory