Skip to content

Conversation

@aljungstrom
Copy link
Contributor

@aljungstrom aljungstrom commented Jul 10, 2025

Sorry, huge PR incoming... The code in this PR is ported from a private repo containing the formalisation of (most of) Cellular Methods in Homotopy Type Theory by me and @loic-p. Since it also contains results that'll be used in the Serre Finiteness formalisation (ping @owen-milner, @rwbarton, @mortberg), I think it belongs in the cubical library.

Key results:

  1. The Hurewicz theorem.: HurewiczTheorem in Cubical/CW/HurewiczTheorem.agda
  2. Homotopy groups of sufficiently connected CW complexes are finitely presented:
    isFinitelyPresented-π'connectedCW in Cubical/CW/Connected.agda
  3. Pushout structure on CW complexes: in Cubical/CW/Instances/Pushout.agda

Detailed overview:

Cubical/Algebra/...

  • Finitely presented abelian groups
  • other minor missing results

Cubical/CW/...

  • Cellular approximation theorem (for finite CW complexes), (Approximation.agda)
  • Renamings (e.g. isCW -> hasCWskel)
  • Characterisation of low-dimensional structure of n-connected CW complexes (Connected.agda)
  • Computations of homology groups of some important spaces (Groups/...)
  • Hurewicz theorem (HurewiczTheorem.agda)
  • CW structure on key constructions such as empty types, pushouts, joins, etc. (Instances/...)
  • Construction of CW complexes and maps with certain strict equalities (Strictification.agda)

Cubical/Data/...

  • Other minor results

Cubical/HITs/...

  • 'Abelianised' path types and their theory (path types with an additional constructor forcing commutativity of path composition). These are used to compute abelianised fundamental groups directly via encode-decode proofs (AbPath/...)
  • Basic results about maps bouquets, pushouts and sequential colimits, sphere bouquets, suspensions and wedge sums.

Cubical/Homotopy/...

  • Connectedness of wedge inclusion (BlakersMassey.agda)
  • Minor results/constructions concerning connectedness and homotopy groups
  • Computation of homotopy groups of Sphere bouquets (Group/PiSphereBouquet.agda)
  • Computation of homotopy groups of cofibres of maps between Sphere bouquets (Group/PiCofibFinSphereBouquetMap.agda)
  • Computation of abelianised homotopy groups of cofibres of maps between Sphere bouquets (Group/PiAbCofibFinSphereBouquetMap.agda)

Copy link
Contributor

@mortberg mortberg left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Just some very minor things. Amazing stuff!

@rwbarton
Copy link
Contributor

rwbarton commented Aug 1, 2025

You can remove {-# OPTIONS --safe #-} from each module since it's now set globally in the .agda-lib file.

# Conflicts:
#	Cubical/CW/Approximation.agda
#	Cubical/CW/Subcomplex.agda
#	Cubical/HITs/SequentialColimit/Base.agda
#	Cubical/HITs/SphereBouquet/Properties.agda
@mortberg mortberg merged commit 3306f5b into agda:master Aug 3, 2025
1 check passed
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

3 participants