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fix(category_theory/abelian/transfer): fix a potential timeout (#15262)
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At `src/category_theory/abelian/transfer.lean` line 149, `abelian_of_adjunction.coimage_iso_image_hom` is on edge of being timed out by any additional simp lemmas, see #15232. This pr squeezed the `simpa` statement.
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jjaassoonn committed Jul 17, 2022
1 parent 4461149 commit 54594da
Showing 1 changed file with 12 additions and 2 deletions.
14 changes: 12 additions & 2 deletions src/category_theory/abelian/transfer.lean
Expand Up @@ -137,10 +137,20 @@ end
local attribute [simp] cokernel_iso coimage_iso_image coimage_iso_image_aux

-- The account of this proof in the Stacks project omits this calculation.
-- Happily it's little effort: our `[ext]` and `[simp]` lemmas only need a little guidance.
lemma coimage_iso_image_hom {X Y : C} (f : X ⟶ Y) :
(coimage_iso_image F G i adj f).hom = abelian.coimage_image_comparison f :=
by { ext, simpa [-functor.map_comp, ←G.map_comp_assoc] using nat_iso.naturality_1 i f, }
begin
ext,
simpa only [←G.map_comp_assoc, coimage_iso_image, nat_iso.inv_inv_app, cokernel_iso,
coimage_iso_image_aux, iso.trans_symm, iso.symm_symm_eq, iso.refl_trans, iso.trans_refl,
iso.trans_hom, iso.symm_hom, cokernel_comp_is_iso_inv, cokernel_epi_comp_inv, as_iso_hom,
functor.map_iso_hom, cokernel_epi_comp_hom, preserves_kernel.iso_hom, kernel_comp_mono_hom,
kernel_is_iso_comp_hom, cokernel_iso_of_eq_hom_comp_desc_assoc, cokernel.π_desc_assoc,
category.assoc, π_comp_cokernel_iso_of_eq_inv_assoc, π_comp_cokernel_comparison_assoc,
kernel.lift_ι, kernel.lift_ι_assoc, kernel_iso_of_eq_hom_comp_ι_assoc,
kernel_comparison_comp_ι_assoc,
abelian.coimage_image_factorisation] using nat_iso.naturality_1 i f
end

end abelian_of_adjunction

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