feat(Algebra/Homology): the homotopy fiber and the path object

[joelriou]

---

• depends on: feat(CategoryTheory/Limits): biprod.opIso #38996

[github-actions]

PR summary 968bc3138a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.HomotopyFiber (new file)	984

---

Declarations diff

+ BinaryBicone.IsBilimit.ofIso
+ BinaryBicone.IsBilimit.op
+ BinaryBiproductData.ofIso
+ BinaryBiproductData.op
+ HasCylinder
+ HasHomotopyFiber
+ HasPathObject
+ biprod.fst_op_opIso_hom
+ biprod.inl_opIso_inv
+ biprod.inr_opIso_inv
+ biprod.opIso
+ biprod.opIso_hom_fst
+ biprod.opIso_hom_snd
+ biprod.opIso_inv_inl_op
+ biprod.opIso_inv_inr_op
+ biprod.snd_op_opIso_hom
+ decidableRelSymm
+ hasBinaryBiproduct_of_iso
+ homotopyEquiv
+ homotopyFiber
+ homotopy₀₁
+ instance (i : α) : HasBinaryBiproduct (K.op.X i) (K.op.X i) := by
+ instance : (opFunctor V c).IsEquivalence := (opEquivalence V c).isEquivalence_functor
+ instance : (opInverse V c).IsEquivalence := (opEquivalence V c).isEquivalence_inverse
+ instance : (unopFunctor V c).IsEquivalence := (unopEquivalence V c).isEquivalence_functor
+ instance : (unopInverse V c).IsEquivalence := (unopEquivalence V c).isEquivalence_inverse
+ instance : HasHomotopyCofiber ((opFunctor C c).map φ.op)
+ instance [HasBinaryBiproducts C] : HasBinaryBiproducts Cᵒᵖ
+ instance [HasBinaryBiproducts C] : HasHomotopyFiber φ
+ instance [K.HasPathObject] :
+ instance {P Q : C} [HasBinaryBiproduct P Q] :
+ lift
+ lift_π₀
+ lift_π₁
+ ofIso
+ pathObject
+ unop
+ ι
+ π₀
+ π₀CompιHomotopy
+ π₀_ι
+ π₁
+ π₁_ι
++ isZero_X
++ op

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

---

No changes to strong technical debt.

No changes to weak technical debt.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(CategoryTheory/Limits): biprod.opIso #38996
  By Dependent Issues (🤖). Happy coding!