Category Theory and Group Theory

A question about the relationship between category theory and group theory led to https://en.wikipedia.org/wiki/Groupoid_object .

A query of groupoid ring led to:

Generalized ring-groupoids
https://pdfs.semanticscholar.org/ad50/bcc3bf7f4dfb1ebb5319644d2f43408c01fd.pdf

" Groupoids.In this section, we introduce the elementary concepts of the groupoid theory.  Then, it is given some recalls about the concept of ring-groupoid which is a ring object in the category of groupoids."

"In other words, a generalized ring groupoid is a generalized ring object in the category of groupoids"


and

https://en.wikipedia.org/wiki/%E2%88%9E-groupoid (infinity groupoid)


Do all of the axioms of a groupoid object apply to string ring theory??