[Merged by Bors] - feat(CategoryTheory/Sites): small 0-hypercovers

[chrisflav]

A w-0-hypercover E is w'-small if there exists an indexing type ι in Type w' and a
restriction map ι → E.I₀ such that the restriction of E to ι is still covering.

This is weaker than E.I₀ being w'-small. For example, every Zariski cover of X : Scheme.{u} is u-small,
because X itself suffices as indexing type.

---

[github-actions]

PR summary 390a0215d1

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Sites.MorphismProperty	775	776	+1 (+0.13%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Sites.MorphismProperty	1

---

Declarations diff

+ Small.Index
+ Small.mem₀
+ Small.restrictFun
+ instance (E : ZeroHypercover.{w} J S) : ZeroHypercover.Small.{max u v} E
+ instance (E : ZeroHypercover.{w} J S) [Small.{w'} E.I₀] : ZeroHypercover.Small.{w'} E
+ instance (E : ZeroHypercover.{w} J S) [ZeroHypercover.Small.{w'} E] {T : C} (f : T ⟶ S)
+ instance (J : Precoverage C) [Small.{w} J] {S : C} (E : ZeroHypercover.{w'} J S) :
+ instance : Precoverage.Small.{u} (precoverage P)
+ instance : Precoverage.Small.{w} P.precoverage
+ presieve₀_restrictIndex_equiv
+ restrictIndex
+ restrictIndexOfSmall
++ Small

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[chrisflav]

Thanks for the suggestions @joelriou!

[joelriou]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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