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$K$-theory revisited
By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic 
$K$-theory. We give a new and direct proof of Suslin’s result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Our descent theorem contains not only Suslin’s result, but also Nisnevich descent of algebraic 
$K$-theory for affine schemes as special cases. Moreover, the role of the Tor-unitality condition becomes very transparent.
