Below we gave the papers in which applications of topos theory to the modern Theoretical Physics are discussed discussed.
  AXIOMATIC THEORY OF RELATIVITY

Guts, A.K.   A topos-theoretic  approach  to the  foundations  of Relativity theory // Soviet Math. Dokl.- 1991.-V.43, No.3.-P.904-907.

    GENERAL THEORY OF RELATIVITY and THEORY OF GRAVITY

Trifonov, V. Linear Solution of the Four-Dimensionality Problem // Europhys. Lett. 1995. V.32, N.8, P.621-626.

Grinkevich, E.B. Synthetic Differential Geometry: A Way to Intuitionistic Models of General Relativity in Toposes. 1996. Preprint gr-qc/9608013

Guts, A.K., Grinkevich, E.B. Toposes in General Theory of Relativity. 1996. Preprint gr-qc/9610073

Guts, A.K.  Intuitionistic Theory of Space-time (russian) // Международная   геометрическая  школа-семинар  памяти Н.В.Ефимова. Тезисы докладов. Абрау-Дюрсо. 27 сентября - 4 октября 1996 года.- Ростов-на Дону, 1996.- С.87-88.

Zvyagintsev, A.A. Pseudo-Euclidean space in model of Synthetic Differential Geometry   (russian) // Mathematical Structures and Modeling. 1998. No. 2. P.34-38.

Guts, A.K., Zvyagintsev, A.A. Solution of the vacuum Einstein equations in Synthetic Differential Geometry of Kock-Lawvere. - Paper: physics/9909016.

Guts, A.K., Zvyagintsev, A.A. Interpretation of intuitionistic solution of the vacuum Einstein equations in smooth topos . - Paper: gr-qc/0001076.

Grinkevich, E.B. Existence of models for the Pseudo-Riemannian spaces in  Synthetic Differential Geometry (russian)  // Mathematical Structures and Modeling. 1999. No. 4. P.15-22.

Guts, A.K. Topos-theoretic model of the Deutsch multiverse //Mathematical Structures and Modeling. 2001. No.8. P.76-90.

        QUANTUM THEORY

Isham, C.J.  Topos Theory and Consistent Histories: The Internal Logic of the Set of all cosistent sets   // Int. Jour. Theor. Phys. 1997. V.36. P.785--814. -  Paper: gr-qc/9607069

Isham, C.J., Butterfield J.  A topos perspective on the Kochen-Specker theorem: I. Quantum states as generalised valuations // Int. Jour. Theor. Phys. 1998. V.37. P.2669-2733. -- Paper: quant-ph/983055

Isham, C.J., Butterfield J.  A topos perspective on the Kochen-Specker theorem: II. Conceptual aspects, and classical analogues // Int. Jour. Theor. Phys. 1999. V.38. P.827--859. quant-ph/980806

Isham, C.J., Butterfield J., Hamilton J.  A topos perspective on the Kochen-Specker theorem: III. // To appear in Int. Jour. Theor. Phys.2000. -- Paper: quant-ph/9911020

Isham, C.J., Butterfield J. Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity // To appear in Found. Phys. 2000 --  Preprint: gr-qc/9910005

Adelman M., Corbett J.V.  Quantum numbers viewed intuitionistially
 
Baez, J.  This Week's Finds in Mathematical Physics (Week 68) - week68.html