Ge-categories, i.e., 2-categores enriched over groupoids seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using ge-categories?

I am especially interested in ge-categories where 1-morphisms are not invertible. I would also appreciate references.

Ge-categories, i.e., categores enriched over groupoids (these are 2-categories where the set of morhisms $HOM(a,b)$ has a groupoid structure) seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using ge-categories?

I am especially interested in ge-categories where 1-morphisms are not invertible. I would also appreciate references.

Ge-categories, i.e., a 2-category enriched over groupoids seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using ge-categories?

I am especially interested in ge-categories where 1-morphisms are not invertible. I would also appreciate references.

Ge-categories, i.e., 2-categores enriched over groupoids seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using ge-categories?

I am especially interested in ge-categories where 1-morphisms are not invertible. I would also appreciate references.

G.e.-categories, i.e., a 2-category enriched over groupoids seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using g.e.-categories?

I am especially interested in e.g. categories where 1-morphisms are not invertible. I would also appreciate references.

Ge-categories, i.e., a 2-category enriched over groupoids seem to be useful in homotopy theory.

Question: What are results in homotopy theory proved using ge-categories?

I am especially interested in ge-categories where 1-morphisms are not invertible. I would also appreciate references.