Multivariable loop spaces

[fredrik-bakke]

Co-authored-by: Mark Williams [email protected]

[VojtechStep]

Do you have a reference for this concept 👀? I'd like to see what the "variables" refer to, and why I should think about non-generalized loop spaces as "bivariable"

[fredrik-bakke]

@VojtechStep No, unfortunately I don't have a reference. This is original work and you can consider the name as merely a working name for now. I suppose part of the motivation is that one wants higher loop spaces to be captured by the same notion, so e.g. an 𝕊¹-ary loop should be a double loop, and that works with this definition of a higher-ary loop space.

[fredrik-bakke]

I can also draw the comparison to that the left-adjoint of loops, suspensions, is the colimit of the binary terminal span.