Theorems · Theorem · category theory
CategoryTheory.GlueData.t_inv
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v, u₁} C] (D : CategoryTheory.GlueData C) (i j : D.J),
CategoryTheory.CategoryStruct.comp (D.t i j) (D.t j i) = CategoryTheory.CategoryStruct.id (D.V (i, j))- Defined in
- Mathlib.CategoryTheory.GlueData
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Limits.pullbackproof · cited by 864
- CategoryTheory.Limits.pullback.fstproof · cited by 639
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- CategoryTheory.invproof · cited by 467
- CategoryTheory.GlueData.Jstatement and proof · cited by 141
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eqproof · cited by 3
- AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'proof · cited by 2
- CategoryTheory.GlueData.t_inv_assocproof · cited by 2
- CategoryTheory.GlueData.t_inv_applyproof · cited by 1
- CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetryproof · cited by 1
- CategoryTheory.GlueData.t'_invproof · cited by 0