Basic theorems in algebraic K-theory

Template:Short description In mathematics, there are several theorems basic to algebraic K-theory.

Throughout, for simplicity, we assume when an exact category is a subcategory of another exact category, we mean it is strictly full subcategory (i.e., isomorphism-closed.)

Theorems

The localization theorem generalizes the localization theorem for abelian categories.

Let $C\subset D$ be exact categories. Then C is said to be cofinal in D if (i) it is closed under extension in D and if (ii) for each object M in D there is an N in D such that $M\oplus N$ is in C. The prototypical example is when C is the category of free modules and D is the category of projective modules.

See also

• Fundamental theorem of algebraic K-theory

Bibliography

• Template:Cite journal
• Ross E. Staffeldt, On Fundamental Theorems of Algebraic K-Theory
• GABE ANGELINI-KNOLL, FUNDAMENTAL THEOREMS OF ALGEBRAIC K-THEORY
• Template:Cite arXiv

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