Commit 2021-04-21 04:20 9b8d6e49
View on Github →feat(category_theory/monoidal): Drinfeld center (#7186)
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:
- Integration with homotopy.io / globular to give "picture proofs".
- 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).
- Automating these proofs using
rewrite_search
or some relative.