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[Merged by Bors] - feat: port CategoryTheory.Quotient #2339
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mpenciak
commented
Feb 17, 2023
currently there are errors in three parts:
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I checked the names and things seem in order now. Two changes that I'd like confirmation on:
/-- A `HomRel` is a congruence when it's an equivalence on every hom-set, and it can be composed
from left and right. -/
class Congruence : Prop where
/-- `r` is an equivalence on every hom-set. -/
isEquiv : ∀ {X Y}, IsEquiv _ (@r X Y)
/-- Precomposition with an arrow respects `r`. -/
compLeft : ∀ {X Y Z} (f : X ⟶ Y) {g g' : Y ⟶ Z}, r g g' → r (f ≫ g) (f ≫ g')
/-- Postcomposition with an arrow respects `r`. -/
compRight : ∀ {X Y Z} {f f' : X ⟶ Y} (g : Y ⟶ Z), r f f' → r (f ≫ g) (f' ≫ g)
#align category_theory.congruence CategoryTheory.Congruence
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In general equalities of functors can be quite taxing on the kernel. And mathematically it isn't a very well-behaved notion anyways. That's why we often only state isomorphisms. |
from left and right. -/ | ||
class Congruence : Prop where | ||
/-- `r` is an equivalence on every hom-set. -/ | ||
isEquiv : ∀ {X Y}, IsEquiv _ (@r X Y) |
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isEquiv
looks good to me.
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Thanks 🎉
bors merge
Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Rémi Bottinelli <remi.bottinelli@bluewin.ch>
Pull request successfully merged into master. Build succeeded:
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