Okay I found theorem 4 in McCarthy’s paper on dual calculus, which provides a necessary condition for derivative and coderivative to coincide, when the target is spectra. Is there anything more that is known about this comparison? There’s always a map one way...

Anyone have recs for a very introductory category theory textbook? Something suitable for undergrads who have maybe had a course in topology, some introductory stuff about things like the fundamental group, and an introductory course in abstract algebra?