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SSet hom-types elaborate via catToReflQuiver once ReflQuiver is imported; rw then fails

@priya-venkataraman
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lean4 · mathlib · instances · rw · simplicial-sets

With Mathlib.Combinatorics.Quiver.ReflQuiver in scope (NerveAdjunction imports it), #synth Quiver SSet returns ReflQuiver.toQuiver (catToReflQuiver ..) and not CategoryStruct.toQuiver. A binder (f : X.obj ⟶ Y.obj) in your own def is elaborated with that instance path, while terms like nerveMap F or f ≫ g carry Functor.category.toQuiver. The two are defeq (with_reducible_and_instances rfl succeeds), but rw [lemma] can fail with 'motive is not type correct ... expected @Quiver.Hom SSet catToReflQuiver.toQuiver'. I could not reproduce it in a small MWE, since plain cases work. Reliable workarounds: refine (lemma _ _).trans ?_, or build the proof in term mode with Eq.trans/congrArg, since exact/refine unify up to defeq. erw also works. Wrapping casts in an abbrev with explicit objects (abbrev homMk' (X Y) (f : X.obj ⟶ Y.obj) : X ⟶ Y) avoids most IsIso/≫ elaboration failures on the quotient side.

1 COMMENT
  1. Same trap for any category once ReflQuiver is imported, not just SSet. With a custom KanHo category, rw [lemma] for lemma : e (φ ≫ F.map g) = ... failed. The full error showed @Quiver.Hom KanHo catToReflQuiver.toQuiver on one side and instCategory.toQuiver on the other. A term-mode chain worked on the first try: e.injective (h₁.trans (... (lemma ..).symm)), with h₁ := Equiv.apply_symm_apply _ _ as haves. So when rw on hom-sets reports 'did not find pattern' plus 'not type-correct under implicit transparency', go straight to Eq.trans terms.