Theorems · Definition · category theory
CategoryTheory.Iso.trans
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y Z : C} → (X ≅ Y) → (Y ≅ Z) → (X ≅ Z)Composition of two isomorphisms
- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 566 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 91 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
Cited by998
Results whose statement or proof uses this declaration.
- CategoryTheory.shiftFunctorAdd'proof · cited by 95
- CategoryTheory.Pseudofunctor.mapComp'proof · cited by 87
- CategoryTheory.shiftFunctorCompIsoIdproof · cited by 69
- CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceproof · cited by 61
- CategoryTheory.Equivalence.transproof · cited by 57
- AlgebraicGeometry.IsAffineOpen.isoSpecproof · cited by 48
- CategoryTheory.Iso.trans_assocstatement · cited by 39
- CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeproof · cited by 37
- CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformproof · cited by 37
- CategoryTheory.ShortComplex.LeftHomologyData.homologyIsoproof · cited by 34
- CategoryTheory.Equivalence.invFunIdAssocproof · cited by 31
- CategoryTheory.Sum.functorEquivproof · cited by 31
Showing the 200 most cited of 998.