Basic theorems in algebraic K-theory: Difference between revisions

Revision as of 01:23, 29 October 2019

Revision as of 01:23, 29 October 2019

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{{math_theorem|name=Additivity theorem<ref>{{harvnb|Weibel|loc=Ch. V, Additivity Theorem 1.2.}}</ref>|Let <math>B, C</math> be exact categories (or other variants). Given a short exact sequence of functors <math>F' \rightarrowtail F \twoheadrightarrow F''</math> from <math>B</math> to <math>C</math>, <math>F_* \simeq F'_* + F''_*</math> as <math>H</math>-space maps; consequently, <math>F_* = F'_* + F''_*: K_i(B) \to K_i(C)</math>.}}

The localization theorem generalizes the [[localization theorem for an abelian categories]].