In this paper, which is the second part of a study of partial map categories with images, we investigate the interaction between images and various other kinds of categorical structure and properties. In particular, we consider images in the context of partial products, meets and discreteness and survey a taxonomy of structures leading towards the partial map categories of regular categories. We also present a term logic for cartesian partial map categories with images and prove a soundness and completeness theorem for this logic. Finally, we exhibit several free constructions relating the different classes of categories under consideration.
Keywords: Categories of partial maps, restriction category, factorization systems
2010 MSC: 18A15, 18A32, 18D20
Theory and Applications of Categories, Vol. 26, 2012, No. 18, pp 453-500.