You mean Goubault-style homotopy stuff. I don't this this is very categorical, e.g. [2] produces a single category, so I wouldn't call this an example of catego

You mean Goubault-style homotopy stuff. I don't this this is very categorical, e.g. [2] produces a single category, so I wouldn't call this an example of categorical structure. The Gunawardena paper [1] doesn't exhibit categorical structure either.