Mac Lane started out in logic before category theory was invented and I think this had a positive influence on his pedagogical style in writing, for example, te

Mac Lane started out in logic before category theory was invented and I think this had a positive influence on his pedagogical style in writing, for example, textbooks. Does what you say have anything to do with probability theory (e.g.: the set space B given that A is true)? There are of course the basic adjunctions that apply to quantifiers and connectives (e.g.: the adjoints to the preimage). Is iteration and nesting as you mention similar to this?