Loogle!

Result

Found 16 declarations mentioning CategoryTheory.Limits.IsColimit.map.

• CategoryTheory.Limits.IsColimit.map 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} (P : CategoryTheory.Limits.IsColimit s) (t : CategoryTheory.Limits.Cocone G) (α : F ⟶ G) : s.pt ⟶ t.pt
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} {t : CategoryTheory.Limits.Cocone G} (P : CategoryTheory.Limits.IsColimit s) (Q : CategoryTheory.Limits.IsColimit t) (w : F ≅ G) : (P.coconePointsIsoOfNatIso Q w).hom = P.map t w.hom
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} {t : CategoryTheory.Limits.Cocone G} (P : CategoryTheory.Limits.IsColimit s) (Q : CategoryTheory.Limits.IsColimit t) (w : F ≅ G) : (P.coconePointsIsoOfNatIso Q w).inv = Q.map s w.inv
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} {r t : CategoryTheory.Limits.Cocone G} (P : CategoryTheory.Limits.IsColimit s) (Q : CategoryTheory.Limits.IsColimit t) (w : F ≅ G) : CategoryTheory.CategoryStruct.comp (P.coconePointsIsoOfNatIso Q w).hom (Q.desc r) = P.map r w.hom
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone G} {r t : CategoryTheory.Limits.Cocone F} (P : CategoryTheory.Limits.IsColimit t) (Q : CategoryTheory.Limits.IsColimit s) (w : F ≅ G) : CategoryTheory.CategoryStruct.comp (P.coconePointsIsoOfNatIso Q w).inv (P.desc r) = Q.map r w.inv
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc_assoc 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone F} {r t : CategoryTheory.Limits.Cocone G} (P : CategoryTheory.Limits.IsColimit s) (Q : CategoryTheory.Limits.IsColimit t) (w : F ≅ G) {Z : C} (h : r.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (P.coconePointsIsoOfNatIso Q w).hom (CategoryTheory.CategoryStruct.comp (Q.desc r) h) = CategoryTheory.CategoryStruct.comp (P.map r w.hom) h
• CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc_assoc 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {s : CategoryTheory.Limits.Cocone G} {r t : CategoryTheory.Limits.Cocone F} (P : CategoryTheory.Limits.IsColimit t) (Q : CategoryTheory.Limits.IsColimit s) (w : F ≅ G) {Z : C} (h : r.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (P.coconePointsIsoOfNatIso Q w).inv (CategoryTheory.CategoryStruct.comp (P.desc r) h) = CategoryTheory.CategoryStruct.comp (Q.map r w.inv) h
• CategoryTheory.Limits.IsColimit.ι_map 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone F} (hc : CategoryTheory.Limits.IsColimit c) (d : CategoryTheory.Limits.Cocone G) (α : F ⟶ G) (j : J) : CategoryTheory.CategoryStruct.comp (c.ι.app j) (hc.map d α) = CategoryTheory.CategoryStruct.comp (α.app j) (d.ι.app j)
• CategoryTheory.Limits.IsColimit.ι_map_assoc 📋 Mathlib.CategoryTheory.Limits.IsLimit
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [CategoryTheory.Category.{v₃, u₃} C] {F G : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone F} (hc : CategoryTheory.Limits.IsColimit c) (d : CategoryTheory.Limits.Cocone G) (α : F ⟶ G) (j : J) {Z : C} (h : d.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (c.ι.app j) (CategoryTheory.CategoryStruct.comp (hc.map d α) h) = CategoryTheory.CategoryStruct.comp (α.app j) (CategoryTheory.CategoryStruct.comp (d.ι.app j) h)
• CategoryTheory.IndParallelPairPresentation.hf 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} {f g : A ⟶ B} (self : CategoryTheory.IndParallelPairPresentation f g) : f = self.isColimit₁.map { pt := B, ι := self.ι₂ } (CategoryTheory.whiskerRight self.φ CategoryTheory.yoneda)
• CategoryTheory.IndParallelPairPresentation.hg 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} {f g : A ⟶ B} (self : CategoryTheory.IndParallelPairPresentation f g) : g = self.isColimit₁.map { pt := B, ι := self.ι₂ } (CategoryTheory.whiskerRight self.ψ CategoryTheory.yoneda)
• CategoryTheory.IndParallelPairPresentation.mk 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} {f g : A ⟶ B} (I : Type v₁) [ℐ : CategoryTheory.SmallCategory I] [hI : CategoryTheory.IsFiltered I] (F₁ F₂ : CategoryTheory.Functor I C) (ι₁ : F₁.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj A) (isColimit₁ : CategoryTheory.Limits.IsColimit { pt := A, ι := ι₁ }) (ι₂ : F₂.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj B) (isColimit₂ : CategoryTheory.Limits.IsColimit { pt := B, ι := ι₂ }) (φ ψ : F₁ ⟶ F₂) (hf : f = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight φ CategoryTheory.yoneda)) (hg : g = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight ψ CategoryTheory.yoneda)) : CategoryTheory.IndParallelPairPresentation f g
• CategoryTheory.IndParallelPairPresentation.mk.sizeOf_spec 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} {f g : A ⟶ B} [SizeOf C] (I : Type v₁) [ℐ : CategoryTheory.SmallCategory I] [hI : CategoryTheory.IsFiltered I] (F₁ F₂ : CategoryTheory.Functor I C) (ι₁ : F₁.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj A) (isColimit₁ : CategoryTheory.Limits.IsColimit { pt := A, ι := ι₁ }) (ι₂ : F₂.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj B) (isColimit₂ : CategoryTheory.Limits.IsColimit { pt := B, ι := ι₂ }) (φ ψ : F₁ ⟶ F₂) (hf : f = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight φ CategoryTheory.yoneda)) (hg : g = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight ψ CategoryTheory.yoneda)) : sizeOf { I := I, ℐ := ℐ, hI := hI, F₁ := F₁, F₂ := F₂, ι₁ := ι₁, isColimit₁ := isColimit₁, ι₂ := ι₂, isColimit₂ := isColimit₂, φ := φ, ψ := ψ, hf := hf, hg := hg } = 1 + sizeOf I + sizeOf ℐ + sizeOf hI + sizeOf F₁ + sizeOf F₂ + sizeOf ι₁ + sizeOf isColimit₁ + sizeOf ι₂ + sizeOf isColimit₂ + sizeOf φ + sizeOf ψ + sizeOf hf + sizeOf hg
• CategoryTheory.IndParallelPairPresentation.mk.injEq 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} {f g : A ⟶ B} (I : Type v₁) [ℐ : CategoryTheory.SmallCategory I] [hI : CategoryTheory.IsFiltered I] (F₁ F₂ : CategoryTheory.Functor I C) (ι₁ : F₁.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj A) (isColimit₁ : CategoryTheory.Limits.IsColimit { pt := A, ι := ι₁ }) (ι₂ : F₂.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I).obj B) (isColimit₂ : CategoryTheory.Limits.IsColimit { pt := B, ι := ι₂ }) (φ ψ : F₁ ⟶ F₂) (hf : f = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight φ CategoryTheory.yoneda)) (hg : g = isColimit₁.map { pt := B, ι := ι₂ } (CategoryTheory.whiskerRight ψ CategoryTheory.yoneda)) (I✝ : Type v₁) (ℐ✝ : CategoryTheory.SmallCategory I✝) (hI✝ : CategoryTheory.IsFiltered I✝) (F₁✝ F₂✝ : CategoryTheory.Functor I✝ C) (ι₁✝ : F₁✝.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I✝).obj A) (isColimit₁✝ : CategoryTheory.Limits.IsColimit { pt := A, ι := ι₁✝ }) (ι₂✝ : F₂✝.comp CategoryTheory.yoneda ⟶ (CategoryTheory.Functor.const I✝).obj B) (isColimit₂✝ : CategoryTheory.Limits.IsColimit { pt := B, ι := ι₂✝ }) (φ✝ ψ✝ : F₁✝ ⟶ F₂✝) (hf✝ : f = isColimit₁✝.map { pt := B, ι := ι₂✝ } (CategoryTheory.whiskerRight φ✝ CategoryTheory.yoneda)) (hg✝ : g = isColimit₁✝.map { pt := B, ι := ι₂✝ } (CategoryTheory.whiskerRight ψ✝ CategoryTheory.yoneda)) : ({ I := I, ℐ := ℐ, hI := hI, F₁ := F₁, F₂ := F₂, ι₁ := ι₁, isColimit₁ := isColimit₁, ι₂ := ι₂, isColimit₂ := isColimit₂, φ := φ, ψ := ψ, hf := hf, hg := hg } = { I := I✝, ℐ := ℐ✝, hI := hI✝, F₁ := F₁✝, F₂ := F₂✝, ι₁ := ι₁✝, isColimit₁ := isColimit₁✝, ι₂ := ι₂✝, isColimit₂ := isColimit₂✝, φ := φ✝, ψ := ψ✝, hf := hf✝, hg := hg✝ }) = (I = I✝ ∧ HEq ℐ ℐ✝ ∧ HEq F₁ F₁✝ ∧ HEq F₂ F₂✝ ∧ HEq ι₁ ι₁✝ ∧ HEq isColimit₁ isColimit₁✝ ∧ HEq ι₂ ι₂✝ ∧ HEq isColimit₂ isColimit₂✝ ∧ HEq φ φ✝ ∧ HEq ψ ψ✝)
• CategoryTheory.NonemptyParallelPairPresentationAux.hf 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} (f g : A ⟶ B) (P₁ : CategoryTheory.Limits.IndObjectPresentation A) (P₂ : CategoryTheory.Limits.IndObjectPresentation B) : f = (CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁ f g P₁ P₂).map { pt := B, ι := CategoryTheory.NonemptyParallelPairPresentationAux.ι₂ f g P₁ P₂ } (CategoryTheory.whiskerRight (CategoryTheory.NonemptyParallelPairPresentationAux.ϕ f g P₁ P₂) CategoryTheory.yoneda)
• CategoryTheory.NonemptyParallelPairPresentationAux.hg 📋 Mathlib.CategoryTheory.Limits.Indization.ParallelPair
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {A B : CategoryTheory.Functor Cᵒᵖ (Type v₁)} (f g : A ⟶ B) (P₁ : CategoryTheory.Limits.IndObjectPresentation A) (P₂ : CategoryTheory.Limits.IndObjectPresentation B) : g = (CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁ f g P₁ P₂).map { pt := B, ι := CategoryTheory.NonemptyParallelPairPresentationAux.ι₂ f g P₁ P₂ } (CategoryTheory.whiskerRight (CategoryTheory.NonemptyParallelPairPresentationAux.ψ f g P₁ P₂) CategoryTheory.yoneda)

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 19971e9 serving mathlib revision 40fea08