chore: deprecate monoidalOfHasFiniteProducts

[YaelDillies]

Over the summer, this was replaced everywhere with CartesianMonoidalCategory.ofHasFiniteProducts, but hadn't been deprecated.

---

I would personally be very happy to also delete the finite coproduct stuff, but we don't yet have cocartesian-monoidal categories to replace them.

[github-actions]

PR summary 7c64d37d34

Import changes exceeding 2%

%	File
+28.04%	Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts	510	653	+143 (+28.04%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts	143

---

Declarations diff

+ instance (X Y : C) :
+++ instance :
- instance (X Y : C) : IsIso (δ F X Y) := by dsimp [δ_eq]; infer_instance
- instance : F.Monoidal := .ofOplaxMonoidal F
- instance : F.OplaxMonoidal
- instance : IsIso (η F) := by dsimp [η_eq]; infer_instance
- leftUnitor_inv
- rightUnitor_inv
- tensorHom
- whiskerLeft
- whiskerRight

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.

---

Increase in tech debt: (relative, absolute) = (0.71, 0.01)

Current number	Change	Type
753	-3	erw
59	1	disabled deprecation lints

Current commit e4f59d6725
Reference commit 7c64d37d34

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).

[joelriou]

In the definition itself, could you use CartesianMonoidalCategory.ofHasFiniteProducts? (using hasFiniteProductsOfHasBinaryAndTerminal).

[YaelDillies]

Sure, although I had to drop the lemmas that are not true anymore