diff --git a/src/simplicial-hott/09-yoneda.rzk.md b/src/simplicial-hott/09-yoneda.rzk.md index 23e6387..50e0e68 100644 --- a/src/simplicial-hott/09-yoneda.rzk.md +++ b/src/simplicial-hott/09-yoneda.rzk.md @@ -1441,15 +1441,14 @@ initial object by `#!rzk is-initial-id-hom-is-segal`. ``` -The other direction is a bit longer. We follow the proof of RS17 9.10: -given `#!rzk (a, u) : Σ (x : A) , C x` an initial object of -`#!rzk Σ (x : A) , C x`, evaluating `#!rzk yon` at `#!rzk u : C a` -yields a family of maps `#!rzk (x : A) → hom A a x → C x`. This is a -contractible map as its fiber at `#!rzk (b : A, v : C b)` is equivalent -to the hom type `#!rzk hom (Σ (x : A) , C x) (a, u) (b, v)` through -the composite of `#!rzk covariant-uniqueness-curried` and -`#!rzk axiom-choice` and it is thus an equivalence using -`#!rzk is-equiv-is-contr-map`. +The other direction is a bit longer. We follow the proof of RS17 9.10: given +`#!rzk (a, u) : Σ (x : A) , C x` an initial object of `#!rzk Σ (x : A) , C x`, +evaluating `#!rzk yon` at `#!rzk u : C a` yields a family of maps +`#!rzk (x : A) → hom A a x → C x`. This is a contractible map as its fiber at +`#!rzk (b : A, v : C b)` is equivalent to the hom type +`#!rzk hom (Σ (x : A) , C x) (a, u) (b, v)` through the composite of +`#!rzk covariant-uniqueness-curried` and `#!rzk axiom-choice` and it is thus an +equivalence using `#!rzk is-equiv-is-contr-map`. ```rzk #def is-representable-family-has-initial-tot @@ -1598,4 +1597,3 @@ the composite of `#!rzk covariant-uniqueness-curried` and ( is-covariant-C) ( has-initial-tot-A)) ``` -