OAI/Algebra/Finitistic/Localization/EvaluationFromAlgebra.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.LittleFinitistic.QuadraticEncoding.Relations.Satisfies line 12

    Source documentation

    The displayed finite list of quadratic equations, in an arbitrary k-algebra.

    def Relations.Satisfies (x : Fin d → R) : Prop := ∀ j,
    …
  2. def OAI.LittleFinitistic.QuadraticEncoding.Representation.ofAction line 20

    Source documentation

    Evaluate the quadratic presentation in any actual algebra action.

    def ofAction (x : Fin d → R) (hx : P.Satisfies x) (ρ : R →ₐ[k] Module.End k Y) :
        Representation P Y where
    …

    Mentions: OAI.LittleFinitistic.QuadraticEncoding.Representation

  3. def OAI.LittleFinitistic.QuadraticEncoding.Representation.ofModule line 28

    Source documentation

    In particular, every R-module supplies the required representation.

    def ofModule (x : Fin d → R) (hx : P.Satisfies x)
        [Module R Y] [IsScalarTower k R Y] : Representation P Y :=
    …

    Mentions: OAI.LittleFinitistic.QuadraticEncoding.Representation

  4. theorem OAI.LittleFinitistic.QuadraticEncoding.Representation.ofModule_generator line 32