Structural Induction and Coinduction in a Fibrational Setting

@article{Hermida1998StructuralIA,
  title={Structural Induction and Coinduction in a Fibrational Setting},
  author={Claudio Hermida and Bart Jacobs},
  journal={Inf. Comput.},
  year={1998},
  volume={145},
  pages={107-152}
}
We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle for terminal coalgebras is admissible. After giving an alternative formulation of induction in terms… 

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