= Mayer-Vietoris sequence in algebraic K-theory
{c}
{title2=$K_1A\to K_1A_1\oplus K_1A_2\to K_1A_0\to K_0A\to K_0A_1\oplus K_0A_2\to K_0A_0$}
The diagonal maps are <extension of scalars>; the maps to $A_0$ are differences. The connecting map sends $g$ to the difference of its patched <free module> and the corresponding free $A$-module. Elementary lifting and common free stabilization prove exactness at every internal term. The displayed fragment does not assert injectivity at its first term or surjectivity at its last.
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