Loogle!

Result

Found 13 declarations mentioning CategoryTheory.Presieve.map.

• CategoryTheory.Presieve.map 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) {X : C} (s : CategoryTheory.Presieve X) : CategoryTheory.Presieve (F.obj X)
• CategoryTheory.Presieve.map_id 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {X : C} (R : CategoryTheory.Presieve X) : CategoryTheory.Presieve.map (CategoryTheory.Functor.id C) R = R
• CategoryTheory.Presieve.map_map 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X Y : C} {f : Y ⟶ X} {R : CategoryTheory.Presieve X} (hf : R f) : CategoryTheory.Presieve.map F R (F.map f)
• CategoryTheory.Presieve.map.of 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X : C} {s : CategoryTheory.Presieve X} {Y : C} {u : Y ⟶ X} (h : s u) : CategoryTheory.Presieve.map F s (F.map u)
• CategoryTheory.Sieve.generate_map_eq_functorPushforward 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) {X : C} {s : CategoryTheory.Presieve X} : CategoryTheory.Sieve.generate (CategoryTheory.Presieve.map F s) = CategoryTheory.Sieve.functorPushforward F (CategoryTheory.Sieve.generate s)
• CategoryTheory.Sieve.arrows_generate_map_eq_functorPushforward 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) {X : C} {s : CategoryTheory.Presieve X} : (CategoryTheory.Sieve.generate (CategoryTheory.Presieve.map F s)).arrows = CategoryTheory.Presieve.functorPushforward F s
• CategoryTheory.Presieve.map_singleton 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X Y : C} (f : X ⟶ Y) : CategoryTheory.Presieve.map F (CategoryTheory.Presieve.singleton f) = CategoryTheory.Presieve.singleton (F.map f)
• CategoryTheory.Presieve.map_ofArrows 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X : C} {ι : Type u_1} {Y : ι → C} (f : (i : ι) → Y i ⟶ X) : CategoryTheory.Presieve.map F (CategoryTheory.Presieve.ofArrows Y f) = CategoryTheory.Presieve.ofArrows (fun i => F.obj (Y i)) fun i => F.map (f i)
• CategoryTheory.Presieve.map_functorPullback 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X : C} (R : CategoryTheory.Presieve (F.obj X)) : CategoryTheory.Presieve.map F (CategoryTheory.Presieve.functorPullback F R) ≤ R
• CategoryTheory.Presieve.map_monotone 📋 Mathlib.CategoryTheory.Sites.Sieves
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {F : CategoryTheory.Functor C D} {X : C} {R S : CategoryTheory.Presieve X} (h : R ≤ S) : CategoryTheory.Presieve.map F R ≤ CategoryTheory.Presieve.map F S
• CategoryTheory.Precoverage.mem_comap_iff 📋 Mathlib.CategoryTheory.Sites.Precoverage
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] {F : CategoryTheory.Functor C D} {J : CategoryTheory.Precoverage D} {X : C} {R : CategoryTheory.Presieve X} : R ∈ (CategoryTheory.Precoverage.comap F J).coverings X ↔ CategoryTheory.Presieve.map F R ∈ J.coverings (F.obj X)
• CategoryTheory.PreZeroHypercover.presieve₀_map 📋 Mathlib.CategoryTheory.Sites.Hypercover.Zero
  {C : Type u} [CategoryTheory.Category.{v, u} C] {S : C} (E : CategoryTheory.PreZeroHypercover S) {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] {F : CategoryTheory.Functor C D} : (CategoryTheory.PreZeroHypercover.map F E).presieve₀ = CategoryTheory.Presieve.map F E.presieve₀
• CategoryTheory.Presieve.map_functorPullback_overForget 📋 Mathlib.CategoryTheory.Sites.Over
  {C : Type u} [CategoryTheory.Category.{v, u} C] {X : C} {Y : CategoryTheory.Over X} (R : CategoryTheory.Presieve Y.left) : CategoryTheory.Presieve.map (CategoryTheory.Over.forget X) (CategoryTheory.Presieve.functorPullback (CategoryTheory.Over.forget X) R) = R

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