More operations on WithOne
and WithZero
#
This file defines various bundled morphisms on WithOne
and WithZero
that were not available in Algebra/Group/WithOne/Defs
.
Main definitions #
WithOne.lift
,WithZero.lift
WithOne.map
,WithZero.map
Equations
- WithOne.instInvolutiveInv = { toInv := WithOne.instInv, inv_inv := ⋯ }
Equations
- WithZero.instInvolutiveNeg = { toNeg := WithZero.instNeg, neg_neg := ⋯ }
WithOne.coe
as a bundled morphism
Equations
- WithOne.coeMulHom = { toFun := WithOne.coe, map_mul' := ⋯ }
Instances For
WithZero.coe
as a bundled morphism
Equations
- WithZero.coeAddHom = { toFun := WithZero.coe, map_add' := ⋯ }
Instances For
Lift a semigroup homomorphism f
to a bundled monoid homomorphism.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Lift an additive semigroup homomorphism f
to a bundled additive monoid homomorphism.
Equations
- One or more equations did not get rendered due to their size.
Instances For
@[simp]
@[simp]
theorem
WithZero.lift_coe
{α : Type u}
{β : Type v}
[Add α]
[AddZeroClass β]
(f : α →ₙ+ β)
(x : α)
:
@[simp]
@[simp]
@[simp]
@[simp]
@[deprecated WithOne.mapMulHom_id (since := "2025-08-26")]
Alias of WithOne.mapMulHom_id
.
@[deprecated WithZero.mapAddHom_id (since := "2025-08-26")]
Alias of WithZero.mapAddHom_id
.
theorem
WithOne.mapMulHom_injective
{α : Type u}
{β : Type v}
[Mul α]
[Mul β]
{f : α →ₙ* β}
(hf : Function.Injective ⇑f)
:
theorem
WithZero.mapAddHom_injective
{α : Type u}
{β : Type v}
[Add α]
[Add β]
{f : α →ₙ+ β}
(hf : Function.Injective ⇑f)
:
@[deprecated WithOne.mapMulHom_injective (since := "2025-08-26")]
theorem
WithOne.map_injective
{α : Type u}
{β : Type v}
[Mul α]
[Mul β]
{f : α →ₙ* β}
(hf : Function.Injective ⇑f)
:
Alias of WithOne.mapMulHom_injective
.
@[deprecated WithZero.mapAddHom_injective (since := "2025-08-26")]
theorem
WithZero.map_injective
{α : Type u}
{β : Type v}
[Add α]
[Add β]
{f : α →ₙ+ β}
(hf : Function.Injective ⇑f)
:
Alias of WithZero.mapAddHom_injective
.
@[deprecated WithOne.mapMulHom_injective' (since := "2025-08-26")]
Alias of WithOne.mapMulHom_injective'
.
@[deprecated WithZero.mapAddHom_injective' (since := "2025-08-26")]
Alias of WithZero.mapAddHom_injective'
.
A version of Equiv.optionCongr
for WithOne
.
Equations
- e.withOneCongr = { toFun := ⇑(WithOne.mapMulHom e.toMulHom), invFun := ⇑(WithOne.mapMulHom e.symm.toMulHom), left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯ }
Instances For
A version of Equiv.optionCongr
for WithZero
.
Equations
- e.withZeroCongr = { toFun := ⇑(WithZero.mapAddHom e.toAddHom), invFun := ⇑(WithZero.mapAddHom e.symm.toAddHom), left_inv := ⋯, right_inv := ⋯, map_add' := ⋯ }
Instances For
@[simp]
@[simp]