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fix: add # to titles in Algebra.Homology.ShortComplex.* (#7062)
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ADedecker authored and kodyvajjha committed Sep 22, 2023
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3 changes: 2 additions & 1 deletion Mathlib/Algebra/Homology/ShortComplex/Homology.lean
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Expand Up @@ -6,7 +6,8 @@ Authors: Joël Riou

import Mathlib.Algebra.Homology.ShortComplex.RightHomology

/-! Homology of short complexes
/-!
# Homology of short complexes
In this file, we shall define the homology of short complexes `S`, i.e. diagrams
`f : X₁ ⟶ X₂` and `g : X₂ ⟶ X₃` such that `f ≫ g = 0`. We shall say that
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5 changes: 3 additions & 2 deletions Mathlib/Algebra/Homology/ShortComplex/LeftHomology.lean
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Expand Up @@ -7,7 +7,8 @@ Authors: Joël Riou
import Mathlib.Algebra.Homology.ShortComplex.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Kernels

/-! LeftHomology of short complexes
/-!
# Left Homology of short complexes
Given a short complex `S : ShortComplex C`, which consists of two composable
maps `f : X₁ ⟶ X₂` and `g : X₂ ⟶ X₃` such that `f ≫ g = 0`, we shall define
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/-- A left homology data for a short complex `S` consists of morphisms `i : K ⟶ S.X₂` and
`π : K ⟶ H` such that `i` identifies `K` to the kernel of `g : S.X₂ ⟶ S.X₃`,
and that `π` identifies `H` to the cokernel of the induced map `f' : S.X₁ ⟶ K` --/
and that `π` identifies `H` to the cokernel of the induced map `f' : S.X₁ ⟶ K` -/
structure LeftHomologyData where
/-- a choice of kernel of `S.g : S.X₂ ⟶ S.X₃`-/
K : C
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5 changes: 3 additions & 2 deletions Mathlib/Algebra/Homology/ShortComplex/RightHomology.lean
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Expand Up @@ -7,7 +7,8 @@ Authors: Joël Riou
import Mathlib.Algebra.Homology.ShortComplex.LeftHomology
import Mathlib.CategoryTheory.Limits.Opposites

/-! RightHomology of short complexes
/-!
# Right Homology of short complexes
In this file, we define the dual notions to those defined in
`Algebra.Homology.ShortComplex.LeftHomology`. In particular, if `S : ShortComplex C` is
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/-- A right homology data for a short complex `S` consists of morphisms `p : S.X₂ ⟶ Q` and
`ι : H ⟶ Q` such that `p` identifies `Q` to the kernel of `f : S.X₁ ⟶ S.X₂`,
and that `ι` identifies `H` to the kernel of the induced map `g' : Q ⟶ S.X₃` --/
and that `ι` identifies `H` to the kernel of the induced map `g' : Q ⟶ S.X₃` -/
structure RightHomologyData where
/-- a choice of cokernel of `S.f : S.X₁ ⟶ S.X₂`-/
Q : C
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