I've been learning about $F$-coalgebras and coinduction from this fantastic paper, which has really helped me get a feel with its many examples. I'm starting to struggle with reconciling the definition of coinduction and proofs-by-coinduction with the way I was taught about induction. I think learning about how induction works for $F$-algebras would really help me as a sort of conceptual bridge, but I can't find any good resources at the level of Rutten's paper that would help me understand. Do you know of any such resources (hopefully replete with plenty of examples)?
Or, perhaps, how does induction work from an $F$-algebraic perspective?