The centric orbit category of a fusion system 
on a finite p-group 
is the full
subcategory 
of the fusion orbit category 
on the 
-centric subgroups (Broto et
al. 2003, Díaz and Park 2015). A subgroup 
of 
is 
-centric if 
for every subgroup 
isomorphic to 
in 
, where 
is the centralizer of
in 
and 
is the group center of 
.
The objects of 
are all subgroups of 
. Its morphisms from 
to 
are the morphisms in 
modulo postcomposition with inner
automorphisms of 
. The centric orbit category retains
these morphisms between its objects. For example, if
is an abelian group, then 
and 
for every subgroup 
, so only 
is 
-centric.
The Díaz-Park sharpness conjecture concerns higher inverse limits over this category
of the contravariant functor part of a Mackey functor on 
(Díaz and Park 2015).
