词条 | Draft:Basic theorems of algebraic K-theory |
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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.) {{math_theorem|name=Additivity theorem|Let}}{{math_theorem|name=Localization theorem|Let}}{{math_theorem|name=Resolution theorem|Let be exact categories. Assume
Then for all .}} Let 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 is in C. The prototypical example is when C is the category of free modules and D is the category of projective modules. {{math_theorem|name=Cofinality theorem|Let}}References
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