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src/library/Abstract/Category/Finitary.hs

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class Category morph => E'PairCofinitary morph where

  -- | Check if the given pair of morphisms \(X \overset{f}{\to} Z
  -- \overset{g}{\leftarrow} Y\) belongs to the class \(\mathcal{E}'\) of joint
  -- surjections. The behaviour is undefined if the given morphisms have
Severity: Minor
Found in src/library/Abstract/Category/Finitary.hs by hlint

Found

class Category morph => E'PairCofinitary morph where
  isJointSurjection :: (morph, morph) -> Bool
  findJointSurjections ::
    (MorphismClass morph, Obj morph)
    -> (MorphismClass morph, Obj morph) -> [(morph, morph)]
  default findJointSurjections ::
            (ECofinitary morph, Cocomplete morph) =>
            (MorphismClass morph, Obj morph)
            -> (MorphismClass morph, Obj morph) -> [(morph, morph)]
  findJointSurjections (c1, x) (c2, y)
    = let (jx, jy) = calculateCoproduct x y
      in
        [(f, g) |
           e <- findAllQuotientsOf (codomain jx),
           let (f, g) = (e <&> jx, e <&> jy),
           f `belongsToClass` c1,
           g `belongsToClass` c2]
  findJointSurjectionSquares ::
    (MorphismClass morph, morph)
    -> (MorphismClass morph, morph) -> [(morph, morph)]
  findJointSurjectionSquares (cf, f) (cg, g)
    = [(f', g') |
         (g', f') <- findJointSurjections (cf, codomain f) (cg, codomain g),
         g' <&> f == f' <&> g]

Perhaps

class Category morph => EPairCofinitary morph where
  isJointSurjection :: (morph, morph) -> Bool
  findJointSurjections ::
    (MorphismClass morph, Obj morph)
    -> (MorphismClass morph, Obj morph) -> [(morph, morph)]
  default findJointSurjections ::
            (ECofinitary morph, Cocomplete morph) =>
            (MorphismClass morph, Obj morph)
            -> (MorphismClass morph, Obj morph) -> [(morph, morph)]
  findJointSurjections (c1, x) (c2, y)
    = let (jx, jy) = calculateCoproduct x y
      in
        [(f, g) |
           e <- findAllQuotientsOf (codomain jx),
           let (f, g) = (e `<&>` jx, e `<&>` jy),
           f `belongsToClass` c1,
           g `belongsToClass` c2]
  findJointSurjectionSquares ::
    (MorphismClass morph, morph)
    -> (MorphismClass morph, morph) -> [(morph, morph)]
  findJointSurjectionSquares (cf, f) (cg, g)
    = [(f', g') |
         (g', f') <- findJointSurjections (cf, codomain f) (cg, codomain g),
         g' `<&>` f `==` f' `<&>` g]

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