Английская Википедия:Basic theorems in algebraic K-theory

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Шаблон: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

Шаблон:Expand section

Шаблон:Math theorem

The localization theorem generalizes the localization theorem for abelian categories.

Шаблон:Math theorem

Шаблон:Math theorem

Let <math>C \subset D</math> 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 <math>M \oplus N</math> is in C. The prototypical example is when C is the category of free modules and D is the category of projective modules.

Шаблон:Math theorem

See also

References

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Шаблон:Algebra-stub