feat(CategoryTheory): group objects

[TwoFX]

Define group objects in cartesian monoidal categories.

Show that the associativity diagram of a group object is always cartesian and deduce that morphisms of group objects commute with taking inverses.

Show that a finite-product-preserving functor takes group objects to group objects.

---

[github-actions]

PR summary a79005572f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_ (new file)	584
Mathlib.CategoryTheory.Monoidal.Grp_ (new file)	609

---

Declarations diff

+ Grp_
+ comp'
+ comp_hom
+ eq_lift_inv_left
+ eq_lift_inv_right
+ forget₂Mon_
+ forget₂Mon_map_hom
+ forget₂Mon_obj_mul
+ forget₂Mon_obj_one
+ fullyFaithfulForget₂Mon_
+ hom_ext
+ id'
+ id_hom
+ instance : (forget₂Mon_ C).Faithful := InducedCategory.faithful _
+ instance : (forget₂Mon_ C).Full := InducedCategory.full _
+ instance : Category (Grp_ C)
+ instance : HasInitial (Grp_ C)
+ instance : Inhabited (Grp_ C)
+ inv_hom
+ isPullback
+ lift_comp_fst_snd
+ lift_comp_inv_left
+ lift_comp_inv_right
+ lift_comp_one_left
+ lift_comp_one_right
+ lift_inv_comp_left
+ lift_inv_comp_right
+ lift_inv_left_eq
+ lift_inv_right_eq
+ lift_leftUnitor_hom
+ lift_lift_assoc
+ lift_lift_associator_hom
+ lift_lift_associator_inv
+ lift_rightUnitor_hom
+ lift_whiskerLeft
+ lift_whiskerRight
+ lift_δ
+ lift_μ
+ mapGrp
+ mkIso
+ mkIso_hom_hom
+ mkIso_inv_hom
+ toUnit_ε
+ trivial
+ uniqueHomFromTrivial
+ δ_fst
+ δ_snd

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).