Example. Weak universality of cpo sums [dt-003A]

Liam O'Connor

Consider this scenario with the cpos $\textbf {2} = \{ \top , \bot \}$ and $\textbf {1} = \{\bot \}$ :

In this case, setting the function

h = \lambda x.\ \top

makes the diagram commute, but

(\lambda x.\ \top ) \neq [\lambda x.\ \top , \lambda x.\ \top ]

due to the different handling of

\bot _{\textbf {1}+\textbf {1}}

.