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View Code? Open in Web Editor NEWCategorical semantics of induction-induction
Categorical semantics of induction-induction
Plan ==== 1. T (Σ A B) ≅ Σ (T A) (□T B) given def. of □T 2. □ for containers = □ for functors 3. Check details of init => elim (e.g. two commuting triangles) 4. Spell out elim => init (need dmap ≅ map) 5. Check that ⟦elim_T⟧_Fam ≅ Elim for simple ind.-ind. 6. Generalise □ and dmap for non-endofunctors, can we derive □G (from □G^?) [need BiAlg closed under Σ] 7. Establish elim ≅ init for the general case 8. Establish laws for □ so we can derive the adhoc eliminators TODO ==== B. Understand equality constraint on G(f, g) better -- how does it appear in def. of dmap_G? C. Uniqueness for elim => init D. Naturality of \phi : FΣ -> Σ□ from inverse image construction? 8. Establish laws for □
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