Last Updated：2022/12/24
A cone is an object (the apex) and a natural transformation from a constant functor (whose image is the apex of the cone and its identity morphism) to a diagram functor. Its components are projections from the apex to the objects of the diagram and it has a “naturality triangle” for each morphism in the diagram. (A “naturality triangle” is just a naturality square which is degenerate at its apex side.)
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A
cone
is
an
object
(the
apex)
and
a
natural
transformation
from
a
constant
functor
(whose
image
is
the
apex
of
the
cone
and
its
identity
morphism)
to
a
diagram
functor.
Its
components
are
projections
from
the
apex
to
the
objects
of
the
diagram
and
it
has
a
“naturality
triangle”
for
each
morphism
in
the
diagram.
(A
“naturality
triangle”
is
just
a
naturality
square
which
is
degenerate
at
its
apex
side.)
