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doc(category/abelian/ext): update module doc (#16512)
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Update future work described in module doc, to reflect previous contributions to mathlib.



Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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semorrison and semorrison committed Sep 16, 2022
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9 changes: 3 additions & 6 deletions src/category_theory/abelian/ext.lean
Expand Up @@ -14,19 +14,16 @@ import category_theory.abelian.projective
# Ext
We define `Ext R C n : Cᵒᵖ ⥤ C ⥤ Module R` for any `R`-linear abelian category `C`
by deriving in the first argument of the bifunctor `(X, Y) ↦ Module.of R (unop X ⟶ Y)`.
by (left) deriving in the first argument of the bifunctor `(X, Y) ↦ Module.of R (unop X ⟶ Y)`.
## Implementation
It's not actually necessary here to assume `C` is abelian,
but the hypotheses, involving both `C` and `Cᵒᵖ`, are quite lengthy,
and in practice the abelian case is hopefully enough.
PROJECT we don't yet have injective resolutions and right derived functors
(although this is only a copy-and-paste dualisation)
so we can't even state the alternative definition
in terms of right-deriving in the first argument,
let alone start the harder project of showing they agree.
PROJECT: State the alternative definition in terms of
right deriving in the second argument, and show these agree.
-/

noncomputable theory
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