G-categories

A G-category is a category on which a group G acts. This work studies the 2-category G -Cat of G-categories, G-functors (functors which commute with the action of G) and G-natural transformations (natural transformations which commute with the G$ action). There is particular emphasis on the relationship between a G-category and its stable subcategory, the largest sub-G-category on which G operates trivially. Also contained here are some very general applications of the theory to various additive G-categories and to G-topoi.