抽象同伦范畴中的局部化

LOCALIZATION FUNCTORS IN ABSTRACT HOMOTOPY CATEGORIES

在抽象同伦范畴中给出了一个局部化函子的存在定理:设C为抽象同伦范畴,S为C中的态类,若(1)存在关于S的左分数范畴;(2)任给si:Xi→Yi(i∈Λ)属于S,有∨si:∨Xi→∨Yi属于S.这里Λ为任一指标集;则存在C上的幂等对(E,η),使得SE=S⊥⊥且DE=S⊥.

A sufficient condition for the existence of idempotent functors in abstract homotopy categories is given. That is: for abstract homotopy categories C, and some class S of morphisms, if(1) there exists a category of left fractions with respect to S; (2) if s_i:X_i→Y_i lies in S for all i∈Λ (here Λ is a set of index), the ∨s_i:∨X_i→∨X_i→∨Y_i lies in S; then there is an idempotent functor (E,η) in C, such that S_E=S^(⊥⊥) and D_E=S^(⊥).