[Merged by Bors] - feat(category_theory/monoidal): Drinfeld center #7186
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Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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Your shortened proofs are still not "pure rewriting proofs", in the sense that that they rewrite by cancellation lemmas which operate on both sides at once. But I don't object. :-) |
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# Half braidings and the Drinfeld center of a monoidal category We define `center C` to be pairs `⟨X, b⟩`, where `X : C` and `b` is a half-braiding on `X`. We show that `center C` is braided monoidal, and provide the monoidal functor `center.forget` from `center C` back to `C`. ## Future work Verifying the various axioms here is done by tedious rewriting. Using the `slice` tactic may make the proofs marginally more readable. More exciting, however, would be to make possible one of the following options: 1. Integration with homotopy.io / globular to give "picture proofs". 2. The monoidal coherence theorem, so we can ignore associators (after which most of these proofs are trivial; I'm unsure if the monoidal coherence theorem is even usable in dependent type theory). 3. Automating these proofs using `rewrite_search` or some relative. Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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Half braidings and the Drinfeld center of a monoidal category
We define
center Cto be pairs⟨X, b⟩, whereX : Candbis a half-braiding onX.We show that
center Cis braided monoidal,and provide the monoidal functor
center.forgetfromcenter Cback toC.Future work
Verifying the various axioms here is done by tedious rewriting.
Using the
slicetactic may make the proofs marginally more readable.More exciting, however, would be to make possible one of the following options:
(after which most of these proofs are trivial;
I'm unsure if the monoidal coherence theorem is even usable in dependent type theory).
rewrite_searchor some relative.