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Reduced homology of CW complexes #1175

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merged 2 commits into from
Mar 4, 2025
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loic-p
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@loic-p loic-p commented Dec 22, 2024

The current definition for the homology of CW complexes is missing its 0-dimensional component. There are two ways to define 0-dimensional homology: "standard" homology and reduced homology.

This commit defines reduced homology for CW complexes:

  • The chain complex associated to a CW presentation is now augmented with Z in dimension -1 [CW/ChainComplex.agda]
  • The chain maps and chain homotopies are extended to work in dimension -1 [CW/Map.agda and CW/Homotopy.agda]
  • The definition of homology in [CW/Homology.agda] is now fed the augmented chain complex. I changed the name from Hᶜʷ to H̃ᶜʷ to match the standard mathematical notation.

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@mortberg mortberg left a comment

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Thanks, looks good to me so will merge!

@mortberg mortberg merged commit 385066b into agda:master Mar 4, 2025
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