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Someone mentioned to me that they had read some books a while ago and forgot the title/author.
Here's what they do remember: It's about dynamical systems and uses category theory. It's from the 1970's approximately. It was a three-volume set. A big punchline was an adjunction. It only concerned itself with linear dynamical systems.
Does anybody have a clue?
There are some references in @fosco's recent paper on automata in species that might be relevant
Oh, Arbib and Manes! I was aware of their work, but I didn't realize it was that old.