VectorBundle.lean`

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

3 declarations, 0 contain sorry, 0 declared as axioms

Imports (3)

Imported by 1 file

FormalConjecturesForMathlib.lean

structure SheafOfModules.VectorBundleData A vector bundle is a sheaf of modules that is locally isomorphic to a free sheaf line 39 source
Source documentation
A vector bundle is a sheaf of modules that is locally isomorphic to a free sheaf.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CategoryTheory.Category, CategoryTheory.GrothendieckTopology, CategoryTheory.Sheaf, RingCat, CategoryTheory.HasWeakSheafify, CategoryTheory.Over, CategoryTheory.GrothendieckTopology.over, AddCommGrpCat, CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective, AddMonoidHom, SheafOfModules
12 instances, coercions and auxiliary constants left out.
```
structure VectorBundleData (M : SheafOfModules.{v} R) where
…
```
structure SheafOfModules.FiniteRankVectorBundleData line 51 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CategoryTheory.Category, CategoryTheory.GrothendieckTopology, CategoryTheory.Sheaf, RingCat, CategoryTheory.HasWeakSheafify, CategoryTheory.Over, CategoryTheory.GrothendieckTopology.over, AddCommGrpCat, CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective, AddMonoidHom, SheafOfModules
12 instances, coercions and auxiliary constants left out.
class SheafOfModules.IsVectorBundleWithRank A class for vector bundles of constant finite rank line 56 source
Source documentation
A class for vector bundles of constant finite rank.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: CategoryTheory.Category, CategoryTheory.GrothendieckTopology, CategoryTheory.Sheaf, RingCat, CategoryTheory.HasWeakSheafify, CategoryTheory.Over, CategoryTheory.GrothendieckTopology.over, AddCommGrpCat, CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective, AddMonoidHom, SheafOfModules, Nat
12 instances, coercions and auxiliary constants left out.
```
class IsVectorBundleWithRank (M : SheafOfModules R) (n : ℕ) where
…
```