Presheaves in category and the twistor approach as the means of description of time irreversibility in various models of space-time

The main topic of the presentation will be the model of the space-time and causal relations based on a category-valued presheaf on the topological Space of Ultimation. The category used is the so-called Quantum Reality category based on C*-algebras. We'll examine in details the concept of the Space of Ultimation, and, particularly, its metric structure. This structure will be investigated using the Twistor Programme. Relationship of the present approach with traditional Quantum Field Theory and, particularly, with Local Quantum Field Theory, will also be considered.
The talk will be based on the preprint http://arxiv.org/abs/1212.5585