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Thibaut Benjamin (May 29 2020 at 15:02):It is well known that monoidal categories are equivalent -categories with one object, and the functor sending a monoidal category onto a category with one object is usually called the delooping. Now as this is an equivalence it has an inverse which sends any one object -category onto its corresponding monoidal category. Is there widely accepted name for this inverse functor?
Gershom (May 29 2020 at 16:15):since delooping is usually defined as the inverse to the loop space construction to begin with, wouldn't the inverse usually be called the "loop space" even if it doesn't land in something we recognize as a typical "space"? Perhaps "loop category"?
Thibaut Benjamin (Jun 01 2020 at 14:37):Thanks, I am having trouble coining the right terminology, but I guess that will do