http://popups.lib.uliege.be/1373-5411/index.php?id=2045 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=2043 Aiming at developing a theoretical framework for the formal study of NP-hard optimisation problems, we have focused on structural properties of optimisation problems related to approximative issue. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, in this work we present a categorical approach to cope with some questions originally studied within Computational Complexity Theory. After defining the polynomial time soluble optimisation problems category OPTS and the optimisation problems category OPT, we introduce a comparison mechanism between them following the basic idea of categorical shape theory, in such way the hierarchical structure of approximation to each optimisation problem can be modelled. Fri, 26 Jul 2024 15:48:26 +0200 Thu, 10 Oct 2024 10:52:10 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2043