Awodey, S. and Birkedal, L. (2003). Elementary axioms for local maps of toposes. Journal of Pure and Applied Algebra 177 (3) 215–230.

Awodey, S., Birkedal, L. and Scott, D. S. (1999). Local realizability toposes and a modal logic for computability: (Extended Abstract). Electronic Notes in Theoretical Computer Science 23 (1) 13–26.

Awodey, S. and Warren, M.A. (2009). Homotopy theoretic models of identity types. Mathematical Proceedings of the Cambridge Philosophical Society 146 (45) 45–55.

Baez, J.C. and Hoffnung, A.E. (2011). Convenient categories of smooth spaces. Transactions of the American Mathematical Society 363 (11) 5789–5825.

Bauer, A. and Lešnik, D. (2012). Metric spaces in synthetic topology. Annals of Pure and Applied Logic 163 (2) 87–100.

Carchedi, D. (2016). On the homotopy type of higher orbifolds and Haefliger classifying spaces. Advances in Mathematics, 294, 756–818. arXiv:1504.02394.

Dubuc, E.J. (1979). Concrete quasitopoi. In: Fourman, M., Mulvey, C. and Scott, D. (eds.) Applications of Sheaves (Proceedings, Durham 1977). Lecture Notes in Mathematics, Springer-Verlag, 239–254.

Dubuc, E.J. and Español, L. (2006). Quasitopoi over a base category. arXiv:math/0612727.

Dubuc, E.J. and Penon, J. (1986). Objets compacts dans les topos. Journal of the Australian Mathematical Society (Series A) 40 (2) 203–217.

Dugger, D. (2001). Universal homotopy theories. Advances in Mathematics 164 (1) 144–176.

Escardó, M.H. and Streicher, T. (2016). The intrinsic topology of Martin-Löf universes. Annals of Pure and Applied Logic 167 (9), 794–805.

Frank, M. (2017). Interpolating between choices for the approximate intermediate value theorem. arXiv:1701.02227.

Gepner, D. and Kock, J. (2012). Univalence in locally cartesian closed (∞, 1)-categories. arXiv:1208.1749.

Goodwillie, T.G. (2003). Calculus. III. Taylor series. Geometry & Topology 7 645–711.

Johnstone, P.T. (1979). On a topological topos. Proceedings of the London Mathematical Society (3) 38 (2) 237–271.

Johnstone, P.T. (2002). Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. Oxford Logic Guides, vol. 43, Oxford Science Publications.

Johnstone, P.T. (2011). Remarks on punctual local connectedness. Theory and Applications of Categories 25 (3) 51–63.

Kapulkin, C. and Lumsdaine, P.L. (2012). The simplicial model of univalent foundations (after Voevodsky). arXiv:1211.2851.

Kraus, N. (2016). Constructions with non-recursive higher inductive types. In: *LICS'16*.

Lawvere, F.W. (1970). Equality in hyperdoctrines and comprehension schema as an adjoint functor. In: Applications of Categorical Algebra, Providence, R.I.: Amer. Math. Soc., pp. 1–14.

Lawvere, F.W. (2007). Axiomatic cohesion. Theory and Applications of Categories 19 (3) 41–49.

Lawvere, F.W. and Menni, M. (2015). Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness. Theory Applications of Categories 30 (26) 909–932.

Licata, D.R. and Shulman, M. (2013). Calculating the fundamental group of the circle in homotopy type theory. In: *LICS'13*. eprint: arXiv:1301.3443.

Licata, D.R., Shulman, M. and Riley, M. (2017). A fibrational framework for substructural and modal logics. To appear in FSCD '17.

Lumsdaine, P.L. and Shulman, M. (2017). Semantics of higher inductive types. arXiv:1705.07088.

Lumsdaine, P.L. and Warren, M.A. (2015). The local universes model: An overlooked coherence construction for dependent type theories. ACM Transactions on Computational Logic 16 (3) 23:1–23:31. arXiv:1411.1736.

Lurie, J. (2009). Higher Topos Theory. Annals of Mathematics Studies, vol. 170, Princeton University Press. arXiv:math.CT/0608040.

Mac Lane, S. and Moerdijk, I. (1994). Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Universitext. Corrected reprint of the 1992 edition. New York: Springer-Verlag.

Menni, M. (2014). Continuous cohesion over sets. Theory and Applications of Categories 29 (20) 542–568.

Palmgren, E. (2007a). A constructive and functorial embedding of locally compact metric spaces into locales. Topology and its Applications 154 (9) 1854–1880.

Palmgren, E. (2007b). Resolution of the Uniform Lower Bound Problem in Constructive Analysis. Tech. rep. 11. Uppsala University Department of Mathematics.

Pfenning, F. and Davies, R. (2001). A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science 11 (4) 511–540.

Rijke, E. (2017). The join construction. arXiv:1701.07538.

Rijke, E., Shulman, M. and Spitters, B. (2017). Modalities in homotopy type theory. arXiv:1706.07526.

Streicher, T. (1991). Semantics of Type Theory: Correctness, Completeness, and Independence Results. Progress in Theoretical Computer Science, Birkhäuser.

Taylor, P. (2010). A lambda calculus for real analysis. Journal of Logic & Analysis 2 (5) 1–115.

Troelstra, A.S. and van Dalen, D. (1988). Constructivism in Mathematics. Vol. I. Studies in Logic and the Foundations of Mathematics, vol. 121. Amsterdam: North-Holland Publishing Co., pp. xx+342+XIV.

van Doorn, F. (2016). Constructing the propositional truncation using non-recursive HITs. In: *Certified Programs and Proofs '16*. arXiv:1512.02274.

Wyler, O. (1991). Lecture Notes on Topoi and Quasitopoi. World Scientific.