Mathlib Map

Theorems · Definition · ring theory

AddMonoidAlgebra.comapDomain

{R : Type u_3} →
  {M : Type u_6} →
    {N : Type u_7} →
      [inst : Semiring R] → (f : M → N) → Function.Injective f → AddMonoidAlgebra R N → AddMonoidAlgebra R M

Pullback the coefficients of an element of R[N] under an injective f : M → N. Coefficients not in the range of f are dropped.

Defined in
Mathlib.Algebra.MonoidAlgebra.MapDomain
Cited by
7 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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AddMonoidAlgebra.coeff_comapDomain · cited by 4AddMonoidAlgebra.coeff_co…AddMonoidAlgebra.comapDomainAddMonoidHom · cited by 3AddMonoidAlgebra.comapDom…AddMonoidAlgebra.comapDomainAddMonoidHom_apply · cited by 1AddMonoidAlgebra.comapDom…AddMonoidAlgebra.comapDomain_single_map · cited by 1AddMonoidAlgebra.comapDom…AddMonoidAlgebra.comapDomain_zero · cited by 0AddMonoidAlgebra.comapDom…AddMonoidAlgebra.comapDomain_add · cited by 0AddMonoidAlgebra.comapDom…AddMonoidAlgebra.mapDomain_comapDomain · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.comapDomain.congr_simp · cited by 0comapDomain.congr_simpSemiring · cited by 13802SemiringAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddMonoidAlgebra.coeff · cited by 365AddMonoidAlgebra.coeffFinsupp.comapDomain · cited by 40Finsupp.comapDomainAddMonoidAlgebra.comapDomainCITED BYCITES

Cites4

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Cited by8

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