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Add documentation for duals #955

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zickgraf opened this issue Jun 27, 2022 · 0 comments
Open

Add documentation for duals #955

zickgraf opened this issue Jun 27, 2022 · 0 comments
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help wanted tasks suited for external help

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@zickgraf
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There are two cases:

  1. In the symmetric closed monoidal case, duals can be defined by an evaluation and a universal property and derived as hom(-,1).
  2. In a symmetric monoidal category, duals can be defined via an evaluation and a coevalution. This sometimes is the definition of "rigid", but not in CAP.

The second case also defines a closed structure and then coincides with the first case. The corresponding derivations are already defined in CAP, the mathematics can be found here: https://mathoverflow.net/questions/141138/definitions-and-coherence-in-rigid-monoidal-categories

Issues which could also be handled in this context: #314 #319 #803

@zickgraf zickgraf added the help wanted tasks suited for external help label Jun 27, 2022
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