| We discuss a concept of loopoid as a non-associative generalization of groupoid. |
| Hence, is a groupoid principal isotope of and is an isomorph of. |
| In the interpreting frames, one would then start from a graded groupoid rather than a monoid. |
| A groupoid is a category in which every morphism is an isomorphism. |
| This groupoid interpretation has been generalized in the following way, which gives an intuitive interpretation of the identity type. |
| Conway introduced the Mathieu groupoid, an extension of the Mathieu group M12 to 13 points. |
