Corrigendum for
---
D. Ahman, T. Uustalu. Decomposing comonad morphisms.
In M. Roggenbach, A. Sokolova, eds., CALCO 2019, v. 139 of LIPIcs,
article 14. Dagstuhl Publishing, 2019. doi:10.4230/lipics.calco.2019.14
---
p 14:6-14:7, Prop 6 and the paragraph preceding it: These statements
are not correct. They should either talk about strong natural
transformations/[co]monad morphisms rather than natural
transformations/[co]monad morphisms or additionally assume that C is
well-pointed (then any functor can have at most one strength and any
natural transformation between two functors is strong wrt their
unique strengths).
Or one can replace the Cartesian closedness assumption of C with the
assumption of presence of small coproducts and to define D^S in Prop 5
as C(S, -) \bullet S (the coproduct of C(S, -) many copies of S)
instead of S \times (S \Rightarrow -), i.e., as the "external" rather
than the "internal" costate functor for S. Then Prop 6 is correct as
it stands. [For the continuation monad, assume small products and
define T^R as C(-, R) \pitchfork R (the product of C(-, R) many copies
of R) rather than (- \Rightarrow R) \Rightarrow R).