Loogle!

Result

Found 14 declarations mentioning CategoryTheory.Presieve.FamilyOfElements.map.

• CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_id 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (x : CategoryTheory.Presieve.FamilyOfElements P R) : x.map (CategoryTheory.CategoryStruct.id P) = x
• CategoryTheory.Presieve.FamilyOfElements.map_id 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (x : CategoryTheory.Presieve.FamilyOfElements P R) : x.map (CategoryTheory.CategoryStruct.id P) = x
• CategoryTheory.Presieve.FamilyOfElements.map 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (p : CategoryTheory.Presieve.FamilyOfElements P R) (φ : P ⟶ Q) : CategoryTheory.Presieve.FamilyOfElements Q R
• CategoryTheory.Presieve.FamilyOfElements.Compatible.compPresheafMap 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (f : P ⟶ Q) {x : CategoryTheory.Presieve.FamilyOfElements P R} (h : x.Compatible) : (x.map f).Compatible
• CategoryTheory.Presieve.FamilyOfElements.Compatible.map 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (f : P ⟶ Q) {x : CategoryTheory.Presieve.FamilyOfElements P R} (h : x.Compatible) : (x.map f).Compatible
• CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.compPresheafMap 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} {x : CategoryTheory.Presieve.FamilyOfElements P R} {t : P.obj (Opposite.op X)} (f : P ⟶ Q) (h : x.IsAmalgamation t) : (x.map f).IsAmalgamation (f.app (Opposite.op X) t)
• CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.map 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} {x : CategoryTheory.Presieve.FamilyOfElements P R} {t : P.obj (Opposite.op X)} (f : P ⟶ Q) (h : x.IsAmalgamation t) : (x.map f).IsAmalgamation (f.app (Opposite.op X) t)
• CategoryTheory.Presieve.FamilyOfElements.map_apply 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (p : CategoryTheory.Presieve.FamilyOfElements P R) (φ : P ⟶ Q) {Y : C} (f : Y ⟶ X) (hf : R f) : p.map φ f hf = φ.app (Opposite.op Y) (p f hf)
• CategoryTheory.Presieve.FamilyOfElements.restrict_map 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (p : CategoryTheory.Presieve.FamilyOfElements P R) (φ : P ⟶ Q) {R' : CategoryTheory.Presieve X} (h : R' ≤ R) : (CategoryTheory.Presieve.FamilyOfElements.restrict h p).map φ = CategoryTheory.Presieve.FamilyOfElements.restrict h (p.map φ)
• CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_comp 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q U : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (x : CategoryTheory.Presieve.FamilyOfElements P R) (f : P ⟶ Q) (g : Q ⟶ U) : (x.map f).map g = x.map (CategoryTheory.CategoryStruct.comp f g)
• CategoryTheory.Presieve.FamilyOfElements.map_comp 📋 Mathlib.CategoryTheory.Sites.IsSheafFor
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {P Q U : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C} {R : CategoryTheory.Presieve X} (x : CategoryTheory.Presieve.FamilyOfElements P R) (f : P ⟶ Q) (g : Q ⟶ U) : (x.map f).map g = x.map (CategoryTheory.CategoryStruct.comp f g)
• CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage 📋 Mathlib.CategoryTheory.Sites.LocallySurjective
  {C : Type u} [CategoryTheory.Category.{v, u} C] {R R' : CategoryTheory.Functor Cᵒᵖ (Type w)} (φ : R ⟶ R') {X : Cᵒᵖ} (r' : R'.obj X) : ((CategoryTheory.Presieve.FamilyOfElements.localPreimage φ r').map φ).IsAmalgamation r'
• CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul 📋 Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C} {R₀ R : CategoryTheory.Functor Cᵒᵖ RingCat} (α : R₀ ⟶ R) [CategoryTheory.Presheaf.IsLocallyInjective J α] {M₀ : PresheafOfModules R₀} {A : CategoryTheory.Functor Cᵒᵖ AddCommGrpCat} (φ : M₀.presheaf ⟶ A) [CategoryTheory.Presheaf.IsLocallyInjective J φ] (hA : CategoryTheory.Presheaf.IsSeparated J A) {X : C} (r : ↑(R.obj (Opposite.op X))) (m : ↑(A.obj (Opposite.op X))) {P : CategoryTheory.Presieve X} (r₀ : CategoryTheory.Presieve.FamilyOfElements (R₀.comp (CategoryTheory.forget RingCat)) P) (m₀ : CategoryTheory.Presieve.FamilyOfElements (M₀.presheaf.comp (CategoryTheory.forget Ab)) P) (hr₀ : (r₀.map (CategoryTheory.Functor.whiskerRight α (CategoryTheory.forget RingCat))).IsAmalgamation r) (hm₀ : (m₀.map (CategoryTheory.Functor.whiskerRight φ (CategoryTheory.forget Ab))).IsAmalgamation m) : ((r₀.smul m₀).map (CategoryTheory.Functor.whiskerRight φ (CategoryTheory.forget Ab))).Compatible
• PresheafOfModules.Sheafify.SMulCandidate.mk' 📋 Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C} {R₀ : CategoryTheory.Functor Cᵒᵖ RingCat} {R : CategoryTheory.Sheaf J RingCat} (α : R₀ ⟶ R.val) [CategoryTheory.Presheaf.IsLocallyInjective J α] {M₀ : PresheafOfModules R₀} {A : CategoryTheory.Sheaf J AddCommGrpCat} (φ : M₀.presheaf ⟶ A.val) [CategoryTheory.Presheaf.IsLocallyInjective J φ] {X : Cᵒᵖ} (r : ↑(R.val.obj X)) (m : ↑(A.val.obj X)) (S : CategoryTheory.Sieve (Opposite.unop X)) (hS : S ∈ J (Opposite.unop X)) (r₀ : CategoryTheory.Presieve.FamilyOfElements (R₀.comp (CategoryTheory.forget RingCat)) S.arrows) (m₀ : CategoryTheory.Presieve.FamilyOfElements (M₀.presheaf.comp (CategoryTheory.forget Ab)) S.arrows) (hr₀ : (r₀.map (CategoryTheory.Functor.whiskerRight α (CategoryTheory.forget RingCat))).IsAmalgamation r) (hm₀ : (m₀.map (CategoryTheory.Functor.whiskerRight φ (CategoryTheory.forget Ab))).IsAmalgamation m) (a : ↑(A.val.obj X)) (ha : ((r₀.smul m₀).map (CategoryTheory.Functor.whiskerRight φ (CategoryTheory.forget Ab))).IsAmalgamation a) : PresheafOfModules.Sheafify.SMulCandidate α φ r m

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision ee8c038 serving mathlib revision 7a9e177