mathlib3
2f29e090 - feat(group_action/defs): generalize faithful actions (#8555)

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4 years ago
feat(group_action/defs): generalize faithful actions (#8555) This generalizes the `faithful_mul_semiring_action` typeclass to a mixin typeclass `has_faithful_scalar`, and provides instances for some simple actions: * `has_faithful_scalar α α` (on cancellative monoids and monoids with zero) * `has_faithful_scalar (opposite α) α` * `has_faithful_scalar α (Π i, f i)` * `has_faithful_scalar (units A) B` * `has_faithful_scalar (equiv.perm α) α` * `has_faithful_scalar M (α × β)` * `has_faithful_scalar R (α →₀ M)` * `has_faithful_scalar S (polynomial R)` (generalized from an existing instance) * `has_faithful_scalar R (mv_polynomial σ S₁)` * `has_faithful_scalar R (monoid_algebra k G)` * `has_faithful_scalar R (add_monoid_algebra k G)` As well as retaining the one other existing instance * `faithful_mul_semiring_action ↥H E` where `H : subgroup (E ≃ₐ[F] E)` The lemmas taking `faithful_mul_semiring_action` as a typeclass argument have been converted to use the new typeclass, but no attempt has been made to weaken their other hypotheses.
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