[Merged by Bors] - feat(group_theory/group_action): Extract a smaller typeclass out of mul_semiring_action
#8918
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…mul_semiring_action` This new typeclass, `mul_distrib_mul_action`, is satisfied by conjugation actions.
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pechersky
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| @@ -2311,6 +2311,10 @@ S.to_submonoid.has_faithful_scalar | |||
| instance [add_monoid α] [distrib_mul_action G α] (S : subgroup G) : distrib_mul_action S α := | |||
| S.to_submonoid.distrib_mul_action | |||
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| /-- The action by a subgroup is the action by the underlying group. -/ | |||
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| /-- The action by a subgroup is the action by the underlying group. -/ | |
| /-- The action by a subgroup is the action by the ambient group. -/ |
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This docstring is copied from lots of other places, so I'd prefer to leave it as is rather than finding all occurences in this PR.
| @@ -855,6 +855,10 @@ lemma smul_def [mul_action M' α] {S : submonoid M'} (g : S) (m : α) : g • m | |||
| instance [add_monoid α] [distrib_mul_action M' α] (S : submonoid M') : distrib_mul_action S α := | |||
| distrib_mul_action.comp_hom _ S.subtype | |||
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| /-- The action by a submonoid is the action by the underlying monoid. -/ | |||
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| /-- The action by a submonoid is the action by the underlying monoid. -/ | |
| /-- The action by a submonoid is the action by the ambient monoid. -/ |
| @@ -960,6 +960,10 @@ S.to_subsemiring.has_faithful_scalar | |||
| instance [add_monoid α] [distrib_mul_action R α] (S : subring R) : distrib_mul_action S α := | |||
| S.to_subsemiring.distrib_mul_action | |||
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| /-- The action by a subsemiring is the action by the underlying semiring. -/ | |||
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| /-- The action by a subsemiring is the action by the underlying semiring. -/ | |
| /-- The action by a subsemiring is the action by the ambient semiring. -/ |
| @@ -819,6 +819,11 @@ S.to_submonoid.has_faithful_scalar | |||
| instance [add_monoid α] [distrib_mul_action R' α] (S : subsemiring R') : distrib_mul_action S α := | |||
| S.to_submonoid.distrib_mul_action | |||
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| /-- The action by a subsemiring is the action by the underlying semiring. -/ | |||
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| /-- The action by a subsemiring is the action by the underlying semiring. -/ | |
| /-- The action by a subsemiring is the action by the ambient semiring. -/ |
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…mul_semiring_action` (#8918) This new typeclass, `mul_distrib_mul_action`, is satisfied by conjugation actions. This PR provides instances for: * `mul_aut` * `prod` of two types with a `mul_distrib_mul_action` * `pi` of types with a `mul_distrib_mul_action` * `units` of types with a `mul_distrib_mul_action` * `ulift` of types with a `mul_distrib_mul_action` * `opposite` of types with a `mul_distrib_mul_action` * `sub(monoid|group|semiring|ring)`s of types with a `mul_distrib_mul_action` * anything already satisfying a `mul_semiring_action`
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This new typeclass,
mul_distrib_mul_action, is satisfied by conjugation actions. This PR provides instances for:mul_autprodof two types with amul_distrib_mul_actionpiof types with amul_distrib_mul_actionunitsof types with amul_distrib_mul_actionuliftof types with amul_distrib_mul_actionoppositeof types with amul_distrib_mul_actionsub(monoid|group|semiring|ring)s of types with amul_distrib_mul_actionmul_semiring_actionThis typeclass was one I suggested in #8592, and is discussed briefly here on Zulip.