Correction to the article An algebraic model for finite loop spaces

We correct here two errors in our earlier paper An algebraic model for finite loop spaces. 55R35; 20D20, 20E22We correct two erroneous arguments found in [3].In the proof of [3, Lemma A.8], we applied [2, Proposition 5.4] to orbit categories of transporter systems, while that proposition is stated only for orbit categories of fusion systems.After replacing that by Proposition 2.3 below, Lemma A.8 can be proven as stated in [3].In the proof of [3, Corollary A.10], we applied [3, Proposition A.9(b)] in a way that is not valid unless all objects in L are F-centric.That corollary is a special case of Proposition 1.6 here. Inclusions of linking systems for the same fusion systemWe refer to [3, Definition 1.9] for the complete definition of a linking system associated to a fusion system F over a discrete p-toral group S .Very briefly, it consists of a category L whose objects are subgroups of S, together with a pair of functors T Ob.L/ .