feat(RingTheory): define R-linear graded algebra homomorphism

[kckennylau]

This PR defines R-linear graded algebra homomorphisms, which are R-algebra homomorphisms that preserve the grading. We also provide the basic properties (aka the "API").

Zulip discussion: #mathlib4 > redefine Graded Algebra

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Split from #26061.

• depends on: feat(Logic): graded functions #30355
• depends on: feat(RingTheory): define graded ring homomorphisms #30312

[github-actions]

PR summary 3540854faa

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.FunLike.GradedFunLike (new file)	220
Mathlib.RingTheory.GradedAlgebra.RingHom (new file)	1093
Mathlib.RingTheory.GradedAlgebra.AlgHom (new file)	1094

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Declarations diff

+ End
+ GradedAlgHom
+ GradedFunLike
+ GradedRingHom
+ algHomClass
+ coeTC
+ coeToRingHom
+ coe_addMonoidHom_injective
+ coe_algHom_injective
+ coe_algHom_mk
+ coe_copy
+ coe_fn_inj
+ coe_fn_injective
+ coe_gRingHom_injective
+ coe_inj
+ coe_linearMap_injective
+ coe_mk'
+ coe_mks
+ coe_monoidHom_injective
+ coe_restrictScalars
+ coe_ringHom_id
+ commutes
+ comp_apply
+ comp_ofId
+ comp_toAlgHom
+ comp_toGRingHom
+ copy
+ copy_eq
+ decompose_map
+ default_apply
+ gradedAddHom
+ gradedFunLike
+ gradedZeroRingHom
+ id_apply
+ id_toAlgHom
+ instCoeOfClass
+ instGradedFunLike
+ instMonoid
+ instMul
+ instOne
+ instRingHomClass
+ mapGraded
+ map_add
+ map_coe_decompose
+ map_mem
+ map_mul
+ map_neg
+ map_one
+ map_sub
+ map_zero
+ mk'
+ mul_def
+ one_def
+ restrictScalars
+ restrictScalars_coe_algHom
+ restrictScalars_coe_linearMap
+ restrictScalars_injective
+ toAddMonoidHom_eq_coe
+ toAlgHom_eq_coe
+ toAlgHom_ofClass
+ toAlgHom_toAddMonoidHom
+ toAlgHom_toMonoidHom
+ toEnd
+ toGRingHom_eq_coe
+ toGRingHom_toAddMonoidHom
+ toGRingHom_toMonoidHom
+ toGradedRingHom_ofClass
+ toMonoidHom_eq_coe
+ toMonoidWithZeroHom_eq_coe
+ toRingHom_eq_coe
+ uniqueOfRight
++ cancel_left
++ cancel_right
++ coe_coe
++ coe_comp
++ coe_id
++ coe_mk
++ coe_mul
++ coe_one
++ coe_pow
++ coe_ringHom_injective
++ comp
++ comp_assoc
++ comp_id
++ congr_arg
++ congr_fun
++ ext
++ id
++ id_comp
++ mk_coe
++ ofClass
++ toFun_eq_coe

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:

• feat(Logic): graded functions #30355
• feat(RingTheory): define graded ring homomorphisms #30312
  By Dependent Issues (🤖). Happy coding!