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feat: quantale homomorphisms #19291
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feat: quantale homomorphisms #19291
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Different bullet style Co-authored-by: Jireh Loreaux <[email protected]>
Style change, including 'left' Co-authored-by: Jireh Loreaux <[email protected]>
…ne.lean to remedy clash on ádd_idem'.
… still is a problem with the doc-string?)
…esiduation to solve doc-string problem in to_additive.
…ify all derived classes. Turned IsIntegral into a mix-in, removed Comm- and Idem- classes as they are now moved to semigroups.
Co-authored-by: Yaël Dillies <[email protected]>
Co-authored-by: Yaël Dillies <[email protected]>
Co-authored-by: Yaël Dillies <[email protected]>
Co-authored-by: Yaël Dillies <[email protected]>
…hile implementing AddQuantaleHom.
PR summary 5189bc2bfdImport changes for modified filesNo significant changes to the import graph Import changes for all files
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Don't know what went wrong on the merge. But now it's gone.
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
…ile. Added QuantaleHom definitions. Note that the doc_strings speak of `AddQuantale` and `Quantale` in anticipation of the variable_alias.
… (Renaming to OrderMulIso should be considered.)
… on Mul. Added proof that any OrderMonoidIso is a QuantaleHom
…r PR. Added a number of theorems inspired by MonoidHom, but frankly I don't understand what I'm doing there yet.
theorem mk_coe (f : α →ₙ*q β) (h) : QuantaleHom.mk (f : α →ₙ* β) h = f := by | ||
ext | ||
rfl |
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theorem mk_coe (f : α →ₙ*q β) (h) : QuantaleHom.mk (f : α →ₙ* β) h = f := by | |
ext | |
rfl | |
theorem mk_coe (f : α →ₙ*q β) (h) : QuantaleHom.mk (f : α →ₙ* β) h = f := rfl |
/-- Reinterpret a quantale homomorphism as a supsemilattice homomorphism-/ | ||
@[to_additive "Reinterpret an additive quantale homomorphism as a supsemilattice homomorphism."] | ||
def toSupBotHom (f : α →ₙ*q β) : SupBotHom α β where | ||
toFun := f | ||
map_sup':= sSupHomClass.toSupBotHomClass.map_sup f | ||
map_bot':= sSupHomClass.toSupBotHomClass.map_bot f | ||
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@[to_additive (attr := simp)] | ||
theorem coe_SupBotHom (f : α →ₙ*q β) : ((f : SupBotHom α β) : α → β) = f := | ||
rfl | ||
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/-- Reinterpret a quantale homomorphism as an order homomorphism. -/ | ||
@[to_additive "Reinterpret an additive quantale homomorphism as an order homomorphism."] | ||
def toOrderHom (f : α →ₙ*q β) : α →o β where | ||
toFun := f | ||
monotone' := by | ||
-- This should not be so elaborate, what am I overlooking? -- | ||
intro x y h | ||
apply le_of_sup_eq | ||
rw [← (f : SupBotHom α β).map_sup'] | ||
dsimp only [toFun_eq_coe] | ||
congr | ||
apply sup_of_le_right | ||
exact h |
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Do you actually need these definitions? They come automatically from sSupHomClass.toSupBotHomClass
and alike
Definition of quantale homomorphisms as functions that are both semigroup homomorphisms and complete lattice homomorphisms.