https://github.com/o-morikawa/highercup

Symbolic manipulation of Steenrod higher cups
https://github.com/o-morikawa/highercup

cup cup-product higher-category-theory higher-cup homotopy homotopy-type-theory steenrod symbolic-mani

Last synced: 5 days ago
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Symbolic manipulation of Steenrod higher cups

• Host: GitHub
• URL: https://github.com/o-morikawa/highercup
• Owner: o-morikawa
• License: mit
• Created: 2024-12-16T15:19:56.000Z (6 days ago)
• Default Branch: main
• Last Pushed: 2024-12-16T15:47:05.000Z (6 days ago)
• Last Synced: 2024-12-16T16:34:31.804Z (6 days ago)
• Topics: cup, cup-product, higher-category-theory, higher-cup, homotopy, homotopy-type-theory, steenrod, symbolic-mani
• Language: Mathematica
• Homepage: https://sites.google.com/view/o-morikawa
• Size: 55.7 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# HigherCup

This is a Mathematica code for computing higher cup products by Steenrod.

Our notation is as follows.

```mathematica

A^{(p)} ⌣_i B^{(q)} ⌣_j C^{(r)}

= Cup[A[p], B[q], C[r]][{i, j}]

```

(Error for wrong numbers of forms and cups.)

Associativity is supported in the appropriate way; an overall factor will be factorized.

The exterior derivative is implemented as $d=$```Del``` as the usual Mathematica code;

here $d$ can act on forms or ```Cup```, which mixes some other forms and higher cups appropriately;

it is surely nilpotent and satisfies homomorphism.

The Leibniz rule holds.