Monoidal bicategories and extensions of gr-categories
Defining the kernel as a homotopy fiber, the author finds the good way to generalize the Schreier-Breen theory. Extensions of gr-categories (i.e., categorical groups or monoidal categories in which all morphisms are iso) are defined and classified. The main result constructs a biequivlence between the 2-category \(\text{Ext}(K,G)^{\text{op}}\) and the bicategory \(\text{Bimon}(K,\text{Bieq}(G))\) of monoidal bicategory homomorphisms between \(K\) and \(\text{Bieq}(G)\), the monoidal bicategory of biequivalences of \(G\) with itself. One has a fundamental work of explicitation, particularly for coherence constraints in monoidal 2-categories.
scientific article; zbMATH DE number 2153129