A categorical approach to injective envelopes

We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the `standard’ operator theoretical definition. An appendix by D. P. Blecher discusses the unitization of an operator space and its injective envelope.