fredriknordvallforsberg / catindind Goto Github PK

Plan
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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
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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 □