Król has been speculating about applications of category theory, topos theory and higher category theory to fundamental physics, notably in the study of gravity, gauge theory quantum gravity and string theory (see also: n-categorical physics).
Jerzy Król Background independence in quantum gravity and forcing constructions Found. of Physics, 34, (2004), 361–403
Jerzy Król Exotic smoothness and non-commutative spaces.the model-theoretic approach Found. of Physics, 34, (2004), 843–869
Jerzy Król Model theory and the AdS/CFT correspondence presented at the IPM String School and Workshop, Queshm Island, Iran, 05–14. 01. 2005, arXiv
Jerzy Król A model for spacetime: The role of interpretation in some grothendieck topoi Found. Phys., 36, (2006), 1070–?
Jerzy Król A model for spacetime ii. the emergence of higher dimensions and field theory/strings dualities Found. Phys., 36 (2006), 1778–?
Jerzy Król Structure of spacetime and topos theory talk presented at 42 nd Karpacz Winter School of Theoretical Physics, Lądek Zdrój, 5–11. 02. 2006, Int. J. Geom. Meth. Mod. Phys. 4 No3, 1–7 (2007)
Jerzy Król Higher YM theories and the compactification in string theory Acta Phys. Polon. B38 (2007) 3641–3646
Jerzy Król Higher symmetry of gravity and the cosmological constant problem PASCOS2008, Waterloo, Kanada, pirsa.org/08060091 (2008).
Jerzy Król $2$-Groups and gravity talk presented at The Jubilee 40th Symposium on Mathematical Physics “Geometry & Quanta” Toruń, June 25–28, 2008