Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 4 (2013), 2335-2346.
Idempotent functors that preserve cofiber sequences and split suspensions
We show that an –localization functor commutes with cofiber sequences of –connected finite complexes if and only if its restriction to the collection of –connected finite complexes is –localization for some unital subring . This leads to a homotopy theoretical characterization of the rationalization functor: the restriction of to simply connected spaces (not just the finite complexes) is rationalization if and only if is nontrivial and simply connected, preserves cofiber sequences of simply connected finite complexes and for each simply connected finite complex , there is a such that splits as a wedge of copies of for various values of .
Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2335-2346.
Received: 21 October 2012
Revised: 15 February 2013
Accepted: 18 February 2013
First available in Project Euclid: 19 December 2017
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Strom, Jeffrey. Idempotent functors that preserve cofiber sequences and split suspensions. Algebr. Geom. Topol. 13 (2013), no. 4, 2335--2346. doi:10.2140/agt.2013.13.2335. https://projecteuclid.org/euclid.agt/1513715641