Kornél Szlachányi is a Hungarian mathematical physicist working in Budapest and teaching also in Pécs.
category list question on flat functors and Grothendieck topologies with Johnstone’s partial answer: gmane
The monoidal Eilenberg-Moore construction and bialgebroids, J. Pure Appl. Algebra 182, 287-315 (2003)
Fiber functors, monoidal sites and Tannaka duality for bialgebroids, arxiv/0907.1578