Jakub Oprsal (ISTA Klosterneuburg, Austria), Topological characterisation of varieties with meet-semidistributive congruences

Tue, 15 Nov 2022, 1:25 pm MST

We will revisit Taylor's 1977 seminal paper `Varieties obeying homotopy laws' through the lens of recent developments in universal algebra and constraint satisfaction problems. The paper studies Maltsev conditions that influence homotopical properties of topological algebras in a variety satisfying such a condition. We recall that a topological algebra is a topological space together with operations that are continuous. Among other insights, we will provide a characterisation of idempotent varieties whose congruence lattices satisfy the meet-semidistributive law in terms of properties of topological algebras in the variety.