feat(Algebra/Category/Grp/Ulift): some properties of the universe lift functor for groups.

[smorel394]

Prove some basic properties of the universe lift functor for groups:

• It is fully faithful.
• It preserves all limits and creates small limits.
• On the category of additive commutative groups, it preserves zero morphisms and is an additive functor.

TODO: colimits.

• depends on: [Merged by Bors] - feat(Algebra/Category/Grp/Limits): the forgetful functor on the category of groups creates all limits #19966

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[github-actions]

PR summary 8ab4216509

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Category.Grp.Ulift (new file)	819

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Declarations diff

+ uliftFunctor_additive
+ uliftFunctor_preservesZeroMorphisms
++ instance : CreatesLimitsOfSize.{w, u} uliftFunctor.{v, u}
++ instance : uliftFunctor.{u, v}.Faithful := Functor.FullyFaithful.faithful uliftFunctorFullyFaithful
++ instance : uliftFunctor.{u, v}.Full := Functor.FullyFaithful.full uliftFunctorFullyFaithful
++ uliftFunctorFullyFaithful
++ uliftFunctor_preservesLimit
++ uliftFunctor_preservesLimitsOfShape
++ uliftFunctor_preservesLimitsOfSize

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.

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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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Algebra/Category/Grp/Limits): the forgetful functor on the category of groups creates all limits #19966
  By Dependent Issues (🤖). Happy coding!