Universal homogeneous objects

Wiesław Kubiś

This page contains information concerning my research on category-theoretic framework for universal homogeneous structures.

Research project: Category-theoretic framework for the Fraissé-Jónsson construction

funded by the National Science Center (Poland), 2011/03/B/ST1/00419

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:

1. Developing the theory of Fraissé-Jónsson limits of singular length.
2. Finding a suitable theory of categories with measures, capturing the case of epsilon-isometries of metric or Banach spaces.
3. Investigating automorphism groups of category-theoretic Fraissé limits.
4. 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.

Works containing results of the project:

1. W. Kubiś, D. Mašulović, Katětov functors [arXiv:1412.1850]
2. W. Kubiś, Metric-enriched categories and approximate Fraïssé limits [arXiv:1210.6506]
3. W. Kubiś, Banach-Mazur game played in partially ordered sets, to appear in Banach Center Publications [arXiv:1505.01094]
4. W. Kubiś, Fraïssé sequences: category-theoretic approach to universal homogeneous structures, Ann. Pure Appl. Logic 165 (2014) 1755--1811 [arXiv:0711.1683]