保持上纤序列和分裂悬置的幂等函子
Idempotent functors that preserve cofiber sequences and split suspensions
摘要：
我们证明了$f$ -局部化函子$L_f$与$(N-1)$ -连通有限复形的上纤维序列交换的充要条件是它对$(N-1)$ -连通有限复形的集合的限制是对某些有单位元的子环$R\sseq\mathbb{Q}$的$R$ -局部化.这导致了有理化函子的同伦理论特征：$L_f$对单连通空间限制（不只是有限复形）是有理化的当且仅当$L_f(S^2)$是非平凡且单连通的，$L_f$保持单连通有限复形的上纤序列，并且对于每个单连通有限复形$K$，对于足够大的$k$和不同的$n$值，$\s^k L_f(K)$分裂为$L_f(S^n)$拷贝的楔形。
英文摘要：
We show that an $f$-localization functor $L_f$ commutes with cofiber sequences of $(N-1)$-connected finite complexes if and only if its restriction to the collection of $(N-1)$-connected finite complexes is $R$-localization for some unital subring $R\sseq\mathbb{Q}$. This leads to a homotopy-theoretical characterization of the rationalization functor: the restriction of $L_f$ to simply-connected spaces (not just the finite complexes) is rationalization if and only if $L_f(S^2)$ is nontrivial and simply-connected, $L_f$ preserves cofiber sequences of simply-connected finite complexes, and for each simply-connected finite complex $K$, $\s^k L_f(K)$ splits as a wedge of copies of $L_f(S^n)$ for large enough $k$ and various values of $n$.
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