We present a version of a proof by Andy Chermak of the existence and uniqueness of centric linking systems associated with arbitrary saturated fusion systems. This proof differs from the one in [Ch2] in that it is based on the computation of derived functors of certain inverse limits. This leads to a much shorter proof, but one which is aimed mostly at researchers familiar with homological algebra.
The author was partially supported by the DNRF through a visiting professorship at the Centre for Symmetry and Deformation in Copenhagen; and also by UMR 7539 of the CNRS and by project ANR BLAN08-2 338236, HGRT.
"Existence and uniqueness of linking systems: Chermak’s proof via obstruction theory." Acta Math. 211 (1) 141 - 175, 2013. https://doi.org/10.1007/s11511-013-0100-3