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Add HasEquivs instance for MatrixCat #2046

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Alizter opened this issue Aug 6, 2024 · 1 comment
Open

Add HasEquivs instance for MatrixCat #2046

Alizter opened this issue Aug 6, 2024 · 1 comment

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@Alizter
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Alizter commented Aug 6, 2024

In theories/Algebra/Rings/Matrix.v we have a definition of the category of matrices whose objects are natural numbers and morhpisms are matrices between those dimensions.

We should add a HasEquivs instance for MatrixCat. It should consist of the following:

  • The type of equivalences will be invertible matrices. That is the subset of matrices which are invertible as ring elements. Theory about invertible ring elements can be found in theories/Algebra/Rings/Ring.v. A sigma type should be enough.
  • The type of "is equivalence" predicates will be if a given matrix is invertible.
  • The other fields of HasEquivs can then be constructed in a straightforward manner using projections and constructors.
@ndcroos
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ndcroos commented Aug 31, 2024

Hi, I am still busy working on the other issues, but I'd like to work on this after these.

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