For the legacy CAP operations of the parametric adjunction $-\otimes a \dashv \mathrm{\underline{Hom}}(a,-)$
EvaluationMorphism($a,b$) is the adjunction counit $(\varepsilon_a)_b: \mathrm{\underline{Hom}}(a,b) \otimes a \rightarrow b$,
CoevaluationMorphism($b,a$) is the adjunction unit $(\eta_a)_b: b \rightarrow \mathrm{\underline{Hom}}(a, b \otimes a)$.
(note: in the documentation of CoevaluationMorphism $a$ and $b$ are permuted)
Contra-intuitively, the first argument $b$ of CoevaluationMorphism is the component while the second is the parameter $a$ of the parametric adjunction. In any case, the orders of the arguments for the unit and the counit are incompatible.
Now that we have the new names ClosedMonoidalLeftEvaluationMorphism etc., I would like to fix this mismatch. If desired I could also change CoevaluationMorphism from currently being a (backward compatibility) synonym of ClosedMonoidalLeftEvaluationMorphism to an operation exhibiting the old flipped order of arguments.
For the legacy CAP operations of the parametric adjunction $-\otimes a \dashv \mathrm{\underline{Hom}}(a,-)$
EvaluationMorphism
($a,b$) is the adjunction counit $(\varepsilon_a)_b: \mathrm{\underline{Hom}}(a,b) \otimes a \rightarrow b$,CoevaluationMorphism
($b,a$) is the adjunction unit $(\eta_a)_b: b \rightarrow \mathrm{\underline{Hom}}(a, b \otimes a)$.(note: in the documentation of
CoevaluationMorphism
$a$ and $b$ are permuted)Contra-intuitively, the first argument $b$ of
CoevaluationMorphism
is the component while the second is the parameter $a$ of the parametric adjunction. In any case, the orders of the arguments for the unit and the counit are incompatible.Now that we have the new names
ClosedMonoidalLeftEvaluationMorphism
etc., I would like to fix this mismatch. If desired I could also changeCoevaluationMorphism
from currently being a (backward compatibility) synonym ofClosedMonoidalLeftEvaluationMorphism
to an operation exhibiting the old flipped order of arguments.