Map · 55
algebraic topology
MSC 55 · Algebraic topology
4,904 declarations (3,471 theorems, 1,433 definitions) across 125 files. 0 of the 14 famous theorems listed for this area are in Mathlib (0%), 1 in some Lean library.
Files are assigned to areas by a language model reading each file's documentation. Report a file that is in the wrong area.
Subareas5
- 55U Applied homological algebra and category theory in algebraic topology 2,410
- 55R Fiber spaces and bundles in algebraic topology 1,193
- 55P Homotopy theory 879
- 55Q Homotopy groups 229
- 55N Homology and cohomology theories in algebraic topology 193
Famous theorems0 of 14
From the 1000+ theorems project, which classifies each theorem by MSC area.
Not yet in Mathlib · 14
Structures defined here24
Typeclasses defined in this area's files, most assumed first.
- FiberBundle 658
- VectorBundle 463
- Topology.RelCWComplex 206
- MemTrivializationAtlas 165
- ContMDiffVectorBundle 142
- Bundle.Trivialization.IsLinear 122
- SSet.Subcomplex.Pairing.IsProper 75
- Topology.CWComplex 54
- SSet.Nonsingular 33
- IsContinuousRiemannianBundle 25
- SSet.HasDimensionLT 25
- Bundle.Pretrivialization.IsLinear 20
- SSet.Finite 20
- Bundle.RiemannianBundle 19
- SSet.Subcomplex.Pairing.IsRegular 15
- SimplyConnectedSpace 14
- ContractibleSpace 11
- SSet.Subcomplex.PairingCore.IsProper 10
- HSpace 7
- Topology.RelCWComplex.Finite 6
- Topology.RelCWComplex.FiniteDimensional 6
- Topology.RelCWComplex.FiniteType 6
- VectorPrebundle.IsContMDiff 6
- SSet.IsStrictSegal 5
Files125
Largest first. The code after each file is its assigned subarea.
- Mathlib.Topology.CWComplex.Classical.Basic
CW complexes
55P · 240
- Mathlib.Topology.FiberBundle.Trivialization
Trivializations
55R · 220
- Mathlib.Topology.VectorBundle.Basic
Vector bundles
55R · 188
- Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
The standard simplex
55U · 145
- Mathlib.Topology.Homotopy.Basic
Homotopy between functions
55P · 138
- Mathlib.Topology.FiberBundle.Basic
Fiber bundles
55R · 129
- Mathlib.AlgebraicTopology.SimplicialObject.Split
Split simplicial objects
55U · 110
- Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal
Strict Segal simplicial sets
55U · 96
- Mathlib.Topology.Homotopy.HomotopyGroup
`n`th homotopy group
55Q · 92
- Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd
A pairing for the pushout-product of a horn inclusion and a boundary inclusion
55U · 90
- Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
The homotopy category of a simplicial set
55P · 89
- Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
The relative cell complex attached to a rank function for a pairing
55U · 88