add missing coherence for TwoOneCat #1897
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theories/WildCat/TwoOneCat.v
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| is1gpd_hom : forall (a b : A), Is1Gpd (a $-> b) ; | ||
| is1functor_postcomp : forall (a b c : A) (g : b $-> c), Is1Functor (cat_postcomp a g) ; | ||
| is1functor_precomp : forall (a b c : A) (f : a $-> b), Is1Functor (cat_precomp c f) ; | ||
| bifunctor_coh_comp : forall {a b c : A} {f f' : a $-> b} {g' g'' : b $-> c} |
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Not sure about this name. We could refactor this after #1886 and ask for composition to be a bifunctor instead.
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I'm also not sure about the direction. I've opted for $@L and $@R first but the other direction would be fine too.
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The name seems ok. I might switch the direction, since the one place it is used, it is in the other direction. It's probably most important to be consistent with Bifunctor.v, if that determines it.
jdchristensen
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I'll look over the rest in a bit.
theories/WildCat/TwoOneCat.v
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| is1gpd_hom : forall (a b : A), Is1Gpd (a $-> b) ; | ||
| is1functor_postcomp : forall (a b c : A) (g : b $-> c), Is1Functor (cat_postcomp a g) ; | ||
| is1functor_precomp : forall (a b c : A) (f : a $-> b), Is1Functor (cat_precomp c f) ; | ||
| bifunctor_coh_comp : forall {a b c : A} {f f' : a $-> b} {g' g'' : b $-> c} |
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The name seems ok. I might switch the direction, since the one place it is used, it is in the other direction. It's probably most important to be consistent with Bifunctor.v, if that determines it.
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The rest LGTM. |
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@jdchristensen I've addressed your comments. |
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LGTM (modulo the build failures). |
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Oops, should be fixed now. I had changed the direction of the coherence but not updated the other files. |
We were missing the bifunctor coherence for composition. This lets us prove the exachange law in a (2,1)-category. Signed-off-by: Ali Caglayan <[email protected]> <!-- ps-id: 3254fcc0-f224-4b14-9c85-5918ad230be1 -->
…omments <!-- ps-id: 7a8dab5b-25d0-4e0d-8341-677ae85964be --> Signed-off-by: Ali Caglayan <[email protected]>
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We were missing the bifunctor coherence for composition. This lets us prove the exchange law in a (2,1)-category.