Loogle!

Result

Found 6 declarations mentioning CategoryTheory.TransfiniteCompositionOfShape.map.

• CategoryTheory.TransfiniteCompositionOfShape.map 📋 Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [OrderBot J] {X Y : C} {f : X ⟶ Y} [SuccOrder J] [WellFoundedLT J] (c : CategoryTheory.TransfiniteCompositionOfShape J f) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] : CategoryTheory.TransfiniteCompositionOfShape J (F.map f)
• CategoryTheory.TransfiniteCompositionOfShape.map_F 📋 Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [OrderBot J] {X Y : C} {f : X ⟶ Y} [SuccOrder J] [WellFoundedLT J] (c : CategoryTheory.TransfiniteCompositionOfShape J f) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] : (c.map F).F = c.F.comp F
• CategoryTheory.TransfiniteCompositionOfShape.map_isoBot 📋 Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [OrderBot J] {X Y : C} {f : X ⟶ Y} [SuccOrder J] [WellFoundedLT J] (c : CategoryTheory.TransfiniteCompositionOfShape J f) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] : (c.map F).isoBot = F.mapIso c.isoBot
• CategoryTheory.TransfiniteCompositionOfShape.map_incl 📋 Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [OrderBot J] {X Y : C} {f : X ⟶ Y} [SuccOrder J] [WellFoundedLT J] (c : CategoryTheory.TransfiniteCompositionOfShape J f) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] : (c.map F).incl = CategoryTheory.CategoryStruct.comp (CategoryTheory.whiskerRight c.incl F) (CategoryTheory.Functor.constComp J Y F).hom
• CategoryTheory.TransfiniteCompositionOfShape.map_isColimit 📋 Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [OrderBot J] {X Y : C} {f : X ⟶ Y} [SuccOrder J] [WellFoundedLT J] (c : CategoryTheory.TransfiniteCompositionOfShape J f) (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] : (c.map F).isColimit = (CategoryTheory.Limits.isColimitOfPreserves F c.isColimit).ofIsoColimit (CategoryTheory.Limits.Cocones.ext (CategoryTheory.Iso.refl (F.mapCocone { pt := Y, ι := c.incl }).pt) ⋯)
• CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_toTransfiniteCompositionOfShape 📋 Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] {J : Type w} [LinearOrder J] [SuccOrder J] [OrderBot J] [WellFoundedLT J] {X Y : C} {f : X ⟶ Y} {W : CategoryTheory.MorphismProperty D} {F : CategoryTheory.Functor C D} [CategoryTheory.Limits.PreservesWellOrderContinuousOfShape J F] [CategoryTheory.Limits.PreservesColimitsOfShape J F] (h : (W.inverseImage F).TransfiniteCompositionOfShape J f) : h.map.toTransfiniteCompositionOfShape = h.map F

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 bce1d65