`constructAssociator`🔗

Definition

Construct the associator morphism or its inverse.

def

constructAssociator (left right ex₀ ey₀ ez₀ : Lean.Expr) (hom : Bool) :
  Lean.MetaM (Lean.Expr × Lean.Expr)
constructAssociator
  (left right ex₀ ey₀ ez₀ : Lean.Expr)
  (hom : Bool) :
  Lean.MetaM (Lean.Expr × Lean.Expr)

Code

def constructAssociator (left right ex₀ ey₀ ez₀ : Expr) (hom : Bool) :
    MetaM (Expr × Expr) := do
  let (X, Y, Z, xLvl, yLvl, zLvl) ← if hom then getTypesFromThreeProds right
    else getTypesFromThreeProds left
  let SX ← computeSFinkerOf X xLvl
  let SY ← computeSFinkerOf Y yLvl
  let SZ ← computeSFinkerOf Z zLvl
  let associator ← mkAppM ``MonoidalCategory.associator #[SX, SY, SZ]
  let associator_hom_proof ←
    if hom then mkAppM ``associator_hom #[SX, SY, SZ, ← idME X, ← idME Y, ← idME Z, ex₀, ey₀, ez₀]
    else mkAppM ``associator_inv #[SX, SY, SZ, ← idME X, ← idME Y, ← idME Z, ex₀, ey₀, ez₀]
  return (← mkAppM (if hom then ``Iso.hom else ``Iso.inv) #[associator], associator_hom_proof)

Actions: Source · Open Issue

Meaning last changed in v4.34.0-rc2-1-g439785b (2026-08-23).

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.

Dependency graph

Audit surface: 4 project declarations, 110 external constants

✓ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.

constructAssociator🔗

`constructAssociator`🔗