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Grantor: National Research Center (Poland)

The main probject objective is to develop the general and applicable theory of Fraissé-Jónsson limits, based on category theory. The project is divided into the following 4 intermediate goals:

- Developing the theory of Fraissé-Jónsson limits of singular length.
- Finding a suitable theory of categories with measures, capturing the case of epsilon-isometries of metric or Banach spaces.
- Investigating automorphism groups of category-theoretic Fraissé limits.
- Studying Fraissé-Jónsson limits of projection-embedding pairs.

Goal 1 aims at better understanding of Fraissé-Jónsson limits induced by ``pushout generated arrows", in particular, when the construction has a singular length. Successful results of Goal 2 will shed more light at objects like the Gurarii space, whose structure and properties are still not well understood. Goal 3 aims at deeper understanding of combinatorial properties of categories related to topological dynamics. Finally, Goal 4 is devoted to the study of important examples of categories related to projections. Particular examples come from domain theory.

IM leader :

Main investigator:

**Kubis** Wieslaw

Participating institutions:

Jan Kochanowski University, Kielce, Poland, **Coordinator**