n (category theory) Given a
diagram F :
J →
C, a
cone consists of an object
N of
C, together with a family of morphisms ψ
X :
N →
F(
X) indexed by all of the objects of
J, such that for every morphism
f :
X →
Y in
J,
. Then
N is the
vertex of the
cone, whose
sides are all the ψ
X indexed by Ob(
J) and whose
base is
F. The
cone is said to be "from
N to
F" and can be denoted as (
N, ψ).