Calin Tataru

Maybe place the inserted signature in a folder.

We could drop the requirement that the orientations sum up to a number between -1 and 1. If we did that, everything would be equipped with a monoid structure (as...

Or we could drop the orientation altogether. Then we wouldn't be able to distinguish f: x -> x and its inverse, but maybe that makes sense in an unoriented setting.

Also what if I wanted to make a 1-cell f into a monoid but my monoid signature is defined on a 0-cell x. We should be able to lift the...

We could also have a feature inside homotopy.io where you can view a library of structures that we have formalised and add them to your signature or a generator with...

I don't see how this is related to functors. This is about adding stuff to the signature.

I don't really see that. You can't send a 1-cell $f$ to the carrier of a monoid object which is 0D.

https://github.com/homotopy-io/homotopy-rs/blob/1680761e96e6c6430597424fd28f10680ab64621/homotopy-web/src/model/proof.rs#L368-L431

The actual enumeration is done by the `embeddings` function which is defined here: https://github.com/homotopy-io/homotopy-rs/blob/1680761e96e6c6430597424fd28f10680ab64621/homotopy-core/src/diagram.rs#L101-L110 https://github.com/homotopy-io/homotopy-rs/blob/1680761e96e6c6430597424fd28f10680ab64621/homotopy-core/src/diagram.rs#L434-L457 And then we filter for the ones that contain the point on this line: https://github.com/homotopy-io/homotopy-rs/blob/1680761e96e6c6430597424fd28f10680ab64621/homotopy-web/src/model/proof.rs#L422

@HdXu can you please upload your workspace with >100 generators and the diagram where it takes a while to list the attachment options. I can then try to run it...