For completeness, a cute factoid is that if we view monoids and groups as categories (that is, [categories with one object] and [categories with one object and every arrow reversible], respectively), then the move from one object to multiple objects creates groupoids from groups and categories from monoids. Hence, categories are monoidoids.
Yep, that turns out to be the case! Jason Gross also pointed this out to me. I didn’t know it when I wrote that, so I guess it’s a good example at least from my perspective.
https://en.wikipedia.org/wiki/Groupoid ?
For completeness, a cute factoid is that if we view monoids and groups as categories (that is, [categories with one object] and [categories with one object and every arrow reversible], respectively), then the move from one object to multiple objects creates groupoids from groups and categories from monoids. Hence, categories are monoidoids.
Yep, that turns out to be the case! Jason Gross also pointed this out to me. I didn’t know it when I wrote that, so I guess it’s a good example at least from my perspective.