I became interested and did not find in one place a list of corresponding terms:
Map <-> Morphism
Foldable <-> Catamorphism
...
Who can supplement the list of terms
I think your question is on the right track but there are so many more ways in which Category Theory connects to other concepts. I also find that relating Category Theory to Type Theory brings more to the table than relating Category Theory to transformations. I say relating, because while Math and Computer Science may use the same terminology, they are not the same; one is not interchangeable with the other.
by John C. Baez and Mike Stay
Category Theory: object X
Computation: data type X
Category Theory: morphism f: X → Y
Computation: program f: X → Y
Category Theory: tensor product of objects: X ⊗ Y
Computation: product of data types: X ⊗ Y
Category Theory: tensor product of morphisms: f ⊗ g
Computation: programs executing in parallel: f ⊗ g
Category Theory: internal hom: X ⊸ Y
Computation: function type: X ⊸ Y
from nLab
Category Theory: counit for hom-tensor adjunction
Type Theory: beta reduction
Category Theory: unit for hom-tensor adjunction
Type Theory: eta conversion
The Yoneda embedding is familiar in category theory. The continuation passing transform is familiar in computer programming. They’re the same thing! Why doesn’t anyone ever say so?
by Mike Stay
There is so much more to this question than can possibly be put into an SO answer.
When I was looking into this in the past I asked most of my questions at StackExchange: Computer Science and updated the most useful references as part of the Category Theory tag. Most of what you seek is found in those references.
If I could have created tables with the SO Markdown I would have added a lot more, but without being in a table seeing them in a list just loses its impact.
If you find Category Theory of interest, then you should also look at HoTT (Homotopy Type Theory)