Differences between framed vs oriented

[calintat]

Reidemeister I move (wire needs to be oriented and invertible):

[calintat]

Every monoid in a braided monoidal category is commutative (both the wire and monoid need to be oriented):

Similarly, given any 3-cell, you can swap any of its inputs/outputs (everything needs to be oriented):

[calintat]

Any invertible monoid gives rise to a Frobenius-like structure (monoid needs to be oriented, wire may be framed):

[NickHu]

Any invertible monoid gives rise to a Frobenius-like structure (monoid needs to be oriented, wire may be framed):

In what sense is this Frobenius? The connectivity between the two wires has been lost

[calintat]

Any invertible monoid gives rise to a Frobenius-like structure (monoid needs to be oriented, wire may be framed):

In what sense is this Frobenius? The connectivity between the two wires has been lost

Yeah I probably shouldn't have called it Frobenius, though it's like a degenerate Frobenious law.

[calintat]

Here is another interesting one...

Given an oriented 2-cell on a (framed) invertible 1-cell, its trace contracts to a scalar version of the 2-cell.

[doctorn]

Here is another interesting one...

Given an oriented 2-cell on a (framed) invertible 1-cell, its trace contracts to a scalar version of the 2-cell.

This is a special case of the contractibility of disks right?

[doctorn]

Fun!

[jamievicary]

Thanks for these great points on this thread. Manuel and I had a long discussion about it. Let's all talk together when you guys are back from FLOC.