group object

1. Definition

Let 20231110-group_object_760824120891fc757bc0445145b027d09b237baa.svg be a monoidal category and 20231110-group_object_c8b0a3b195a2049206595c9a19c3ee1b4c7c0fbb.svg an object Then 20231110-group_object_e6ea90f93286d6ba483e07a608709f47e085e21a.svg is a group object, if

  1. 20231110-group_object_e6ea90f93286d6ba483e07a608709f47e085e21a.svg is a monoid object
  2. there exists a morphisms 20231110-group_object_86cd0cedf8108d22351cf8c7be4d69f64e8ce6e0.svg making
20231110-group_object_5a8b6bb332c5ea769de2160a24aec97d630038d9.svg

and

20231110-group_object_fbaa8c05ef7957ab2c54c83ed8598b3814db13a1.svg

commute, where a) 20231110-group_object_aa699af8b052820cdd98bf8bee54004084151ed7.svg is the unit b) 20231110-group_object_7a1d959981156c1587751c0cb5beba5caad360f8.svg the multiplication c) 20231110-group_object_d3445250b76733db630d51aef463b4729b8c0425.svg the diagonal morphism

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 19:07