Loogle!

Result

Found 11 declarations mentioning CategoryTheory.Limits.IsLimit.map.

• CategoryTheory.Limits.IsLimit.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.Cone F) {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit t) (α : F ⟶ G) : s.pt ⟶ t.pt
• CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_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.Cone F} {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit s) (Q : CategoryTheory.Limits.IsLimit t) (w : F ≅ G) : (P.conePointsIsoOfNatIso Q w).hom = CategoryTheory.Limits.IsLimit.map s Q w.hom
• CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_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.Cone F} {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit s) (Q : CategoryTheory.Limits.IsLimit t) (w : F ≅ G) : (P.conePointsIsoOfNatIso Q w).inv = CategoryTheory.Limits.IsLimit.map t P w.inv
• CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_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} {r s : CategoryTheory.Limits.Cone F} {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit s) (Q : CategoryTheory.Limits.IsLimit t) (w : F ≅ G) : CategoryTheory.CategoryStruct.comp (P.lift r) (P.conePointsIsoOfNatIso Q w).hom = CategoryTheory.Limits.IsLimit.map r Q w.hom
• CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_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} {r s : CategoryTheory.Limits.Cone G} {t : CategoryTheory.Limits.Cone F} (P : CategoryTheory.Limits.IsLimit t) (Q : CategoryTheory.Limits.IsLimit s) (w : F ≅ G) : CategoryTheory.CategoryStruct.comp (Q.lift r) (P.conePointsIsoOfNatIso Q w).inv = CategoryTheory.Limits.IsLimit.map r P w.inv
• CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom_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} {r s : CategoryTheory.Limits.Cone F} {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit s) (Q : CategoryTheory.Limits.IsLimit t) (w : F ≅ G) {Z : C} (h : t.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (P.lift r) (CategoryTheory.CategoryStruct.comp (P.conePointsIsoOfNatIso Q w).hom h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.IsLimit.map r Q w.hom) h
• CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv_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} {r s : CategoryTheory.Limits.Cone G} {t : CategoryTheory.Limits.Cone F} (P : CategoryTheory.Limits.IsLimit t) (Q : CategoryTheory.Limits.IsLimit s) (w : F ≅ G) {Z : C} (h : t.pt ⟶ Z) : CategoryTheory.CategoryStruct.comp (Q.lift r) (CategoryTheory.CategoryStruct.comp (P.conePointsIsoOfNatIso Q w).inv h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.IsLimit.map r P w.inv) h
• CategoryTheory.Limits.IsLimit.map_π_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.Cone F) {d : CategoryTheory.Limits.Cone G} (hd : CategoryTheory.Limits.IsLimit d) (α : F ⟶ G) (j : J) {Z : C} (h : G.obj j ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.IsLimit.map c hd α) (CategoryTheory.CategoryStruct.comp (d.π.app j) h) = CategoryTheory.CategoryStruct.comp (c.π.app j) (CategoryTheory.CategoryStruct.comp (α.app j) h)
• CategoryTheory.Limits.IsLimit.map_π 📋 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.Cone F) {d : CategoryTheory.Limits.Cone G} (hd : CategoryTheory.Limits.IsLimit d) (α : F ⟶ G) (j : J) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.IsLimit.map c hd α) (d.π.app j) = CategoryTheory.CategoryStruct.comp (c.π.app j) (α.app j)
• CategoryTheory.Limits.limMap.eq_1 📋 Mathlib.Condensed.Light.Epi
  {J : Type u₁} [CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [CategoryTheory.Category.{v, u} C] {F G : CategoryTheory.Functor J C} [CategoryTheory.Limits.HasLimit F] [CategoryTheory.Limits.HasLimit G] (α : F ⟶ G) : CategoryTheory.Limits.limMap α = CategoryTheory.Limits.IsLimit.map (CategoryTheory.Limits.limit.cone F) (CategoryTheory.Limits.limit.isLimit G) α
• CategoryTheory.Limits.IsLimit.map.eq_1 📋 Mathlib.Condensed.Light.Epi
  {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.Cone F) {t : CategoryTheory.Limits.Cone G} (P : CategoryTheory.Limits.IsLimit t) (α : F ⟶ G) : CategoryTheory.Limits.IsLimit.map s P α = P.lift ((CategoryTheory.Limits.Cones.postcompose α).obj s)

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