An endofunctor is called pointed if it is equipped with a natural transformation from the identity functor.
(Beware that is not quite the notion of a pointed object in the endo-functor category, since the identity functor is not in general a terminal object there. See the remark there.)
The dual notion is known as a well-copointed endofunctor.
Well-pointed endofunctors have a particularly well-behaved free algebra sequence; see transfinite construction of free algebras.
Well-pointed endofunctors were studied already under the name “symmetric unads” in:
The modern terminology is due to:
Last revised on July 8, 2025 at 15:54:36. See the history of this page for a list of all contributions to it.