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@book{johnstone:elephant,
author = {Johnstone, P. T.},
title = {Sketches of an Elephant: A Topos Theory Compendium},
year = {2002},
publisher = {Oxford University Press}}
@book{johnstone:topos-theory,
author = {Johnstone, P. T.},
title = {Topos Theory},
year = {1977},
series = {L.M.S. Monographs},
volume = {10},
publisher = {Academic Press}}
@article{leinster:introduction,
author = {Leinster, T.},
title = {An informal introduction to topos theory},
journal = {Publications of the nLab},
volume = {1},
number = {1},
year = {2011}}
@inbook{vickers:locales-toposes,
author = {Vickers, S.},
title = {Locales and Toposes as Spaces},
year = {2007},
pages = {429--496},
booktitle = {Handbook of Spatial Logics},
publisher = {Springer},
editor = {Aiello, M. and Pratt-Hartmann, I. and van Benthem, J.},
url = {https://www.cs.bham.ac.uk/~sjv/LocTopSpaces.pdf}}
@article{vickers:continuity,
author = {Vickers, S.},
title = {Continuity and geometric logic},
volume = {12},
number = {1},
year = {2014},
pages = {14--27},
journal = {J. Appl. Log.},
url = {https://www.cs.bham.ac.uk/~sjv/GeoAspects.pdf}}
@article{vickers:case-study,
author = {Vickers, S.},
title = {The double powerlocale and exponentiation: a case study in geometric logic},
year = {2004},
journal = {Theory Appl. Categ.},
volume = {12},
number = {13},
pages = {372--422}}
@inproceedings{mulvey:repr,
author = {Mulvey, C.},
title = {Intuitionistic algebra and representations of rings},
booktitle = {Recent Advances in the Representation Theory of Rings and $C^*$-algebras by Continuous Sections},
year = {1974},
editor = {Hofmann, K. H. and Liukkonen, J. R.},
series = {Mem. Amer. Math. Soc.},
volume = {148},
publisher = {American Mathematical Society},
pages = {3--57}}
@inproceedings{wraith:generic-galois-theory,
author = {Wraith, G.},
title = {Generic Galois theory of local rings},
booktitle = {Applications of sheaves},
year = {1979},
editor = {Fourman, M. and Mulvey, C. and Scott, D.},
series = {Lecture Notes in Math.},
volume = {753},
publisher = {Springer},
pages = {739--767}}
@unpublished{shulman:stack,
author = {Shulman, M.},
title = {Stack semantics and the comparison of material and structural set theories},
year = {2010},
url = {https://arxiv.org/abs/1004.3802}}
@unpublished{shulman:set-theory,
author = {Shulman, M.},
title = {Set theory for category theory},
year = {2008},
url = {https://arxiv.org/abs/0810.1279}}
@inproceedings{feferman:set-foundations,
author = {Feferman, S.},
title = {Set-theoretical foundations of category theory},
booktitle = {Reports of the Midwest Category Seminar~III},
year = {1969},
series = {Lecture Notes in Math.},
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publisher = {Springer},
pages = {201--247}}
@book{troelstra-dalen:constructivism,
author = {Troelstra, A. S. and van Dalen, D.},
title = {Constructivism in Mathematics: An Introduction},
year = {1988},
publisher = {North-Holland Publishing}}
@misc{stacks-project,
author = "The {Stacks Project Authors}",
title = "{Stacks Project}",
url = {https://stacks.math.columbia.edu/}}
@book{moerdijk-maclane:sheaves-logic,
author = {Mac Lane, S. and Moerdijk, I.},
title = {Sheaves in Geometry and Logic: a First Introduction to Topos Theory},
publisher = {Springer},
series = {Universitext},
year = {1992}}
@book{mines-richman-ruitenburg:constructive-algebra,
title = {A Course in Constructive Algebra},
author = {Mines, R. and Richman, F. and Ruitenburg, W.},
series = {Universitext},
year = {1988},
publisher = {Springer}}
@article{richman:noetherian,
title = {The ascending tree condition: constructive algebra without choice},
author = {Richman, F.},
journal = {Comm. Algebra},
volume = {31},
number = {4},
pages = {1993--2002},
year = {2003}}
@book{bishop-bridges:constructive-analysis,
author = {Bishop, E. and Bridges, D.},
title = {Constructive Analysis},
publisher = {Springer},
year = {1985}}
@incollection{bauer:int-mathematics,
author = {Bauer, A.},
title = {Intuitionistic Mathematics and Realizability in the Physical World},
booktitle = {A Computable Universe},
publisher = {World Scientific Pub Co},
editor = {Zenil, H.},
year = {2012}}
@misc{bauer:video,
author = {Bauer, A.},
title = {Five Stages of Accepting Constructive Mathematics},
note = {Lecture at the Institute for Advanced Study},
year = {2013},
url = {https://video.ias.edu/members/1213/0318-AndrejBauer}}
@article{awodey-bauer:bracket,
title = {Propositions as [Types]},
author = {Awodey, S. and Bauer, A.},
journal = {J. Logic Comput.},
volume = {14},
number = {4},
pages = {447--471},
year = {2004}}
@inbook{bell:catlogprime,
author = {Bell, J.},
title = {The development of categorical logic},
editor = {Gabbay, D. and Guenthner, F.},
booktitle = {Handbook of Philosophical Logic},
publisher = {Springer},
edition = {2},
year = {2005},
volume = {12},
pages = {279--361}}
@book{vakil:foag,
author = {Vakil, Ravi},
title = {The Rising Sea. Foundations of Algebraic Geometry},
year = {2017},
url = {http://math.stanford.edu/~vakil/216blog/}}
@article{kleiman:misconceptions,
author = {Kleiman, S.},
title = {Misconceptions about $K_X$},
year = {1979},
volume = {25},
journal = {Enseign. Math.},
pages = {203--206}}
@article{bohr1,
author = {Butterfield, J. and Hamilton, J. and Isham, C.},
title = {A topos perspective on the Kochen--Specker theorem, I. quantum states as generalized valuations},
journal = {Internat. J. Theoret. Phys.},
volume = {37},
number = {11},
pages = {2669--2733},
year = {1998}}
@article{bohr2,
year = {2009},
journal = {Comm. Math. Phys.},
volume = {291},
number = {1},
title = {A topos for algebraic quantum theory},
publisher = {Springer},
author = {Heunen, C. and Landsman, N. and Spitters, B.},
pages = {63--110}}
@misc{bohr3,
author = {Henry, S.},
title = {A geometric Bohr topos},
year = {2015},
url = {https://arxiv.org/abs/1502.01896}}
@article{vries:sheafification,
year = {1987},
author = {de Vries, F.-J.},
title = {Applications of constructive logic to sheaf constructions in toposes},
volume = {25},
journal = {Logic Group preprint series, Rijksuniversiteit Utrecht}}
@inproceedings{johnstone:art,
title = {The art of pointless thinking: a student's guide to the category of locales},
author = {Johnstone, P. T.},
booktitle = {Category theory at work (Bremen, 1990)},
pages = {85--107},
series = {Res. Exp. Math.},
number = {18},
publisher = {Heldermann},
year = {1991}}
@article{johnstone:point,
title = {The point of pointless topology},
author = {Johnstone, P. T.},
year = {1983},
journal = {Bull. Amer. Math. Soc.},
volume = {8},
number = {1},
pages = {41--53}}
@inbook{dyn:char-krull,
author = {Coquand, T. and Lombardi, H. and Roy, M.-F.},
booktitle = {From Sets and Types to Analysis and Topology: Towards Practicable Foundations for Constructive Mathematics},
publisher = {Oxford Univ. Press},
year = {2005},
title = {An elementary characterisation of Krull dimension},
pages = {239--244}}
@article{dyn:krull-integral,
author = {Coquand, T. and Ducos, L. and Lombardi, H. and Quitté, C.},
title = {Constructive Krull dimension I: integral extensions},
journal = {J. Algebra Appl.},
volume = {8},
number = {1},
pages = {129-138},
year = {2009}}
@article{dyn:krull-dim-polynomial-ring,
author = {Coquand, T. and Lombardi, H.},
title = {A short proof for the Krull dimension of a polynomial ring},
journal = {Amer. Math. Monthly},
volume = {112},
number = {9},
year = {2005},
pages = {826--829}}
@article{gillam:localization,
author = {Gillam, W. D.},
title = {Localization of ringed spaces},
journal = {Adv. Pure Math.},
volume = {1},
number = {5},
pages = {250--263},
year = {2011}}
@book{hakim:relative-schemes,
author = {Hakim, M.},
title = {Topos annelés et schémas relatifs},
series = {Ergeb. Math. Grenzgeb.},
volume = {64},
year = {1972},
publisher = {Springer}}
@phdthesis{jackson:sheaf-theoretic-measure-theory,
author = {Jackson, M.},
title = {A sheaf theoretic approach to measure theory},
year = {2006},
school = {University of Pittsburgh}}
@article{aczel:russell-prawitz,
author = {Aczel, P.},
title = {The Russell--Prawitz modality},
year = {2001},
journal = {Math. Structures Comput. Sci},
volume = {11},
number = {4},
pages = {541--554}}
@inproceedings{escardo:oliva:peirce-shift,
author = {Escardó, M. and Oliva, P.},
title = {The Peirce translation and the double negation shift},
year = {2010},
booktitle = {Programs, Proofs, Processes},
series = {Lecture Notes in Comput. Sci.},
volume = {6158},
editor = {Ferreira, F. and Löwe, B. and Mayordomo, E. and Mendes Gomes, L.},
publisher = {Springer},
pages = {151--161}}
@unpublished{lurie:dag5,
author = {Lurie, J.},
title = {Derived Algebraic Geometry V: Structured Spaces},
year = {2009},
url = {https://arxiv.org/abs/0905.0459}}
@misc{tao:analysis-rel-measure-space,
author = {Tao, T.},
title = {Real analysis relative to a finite measure space},
year = {2014},
url = {https://terrytao.wordpress.com/2014/07/15/real-analysis-relative-to-a-finite-measure-space/}}
@misc{tao:cheap-nsa,
author = {Tao, T.},
title = {A cheap version of nonstandard analysis},
year = {2012},
url = {https://terrytao.wordpress.com/2012/04/02/a-cheap-version-of-nonstandard-analysis/}}
@book{kock:sdg,
author = {Kock, A.},
title = {Synthetic Differential Geometry},
year = {2006},
publisher = {Cambridge University Press},
edition = {2},
series = {London Math Soc. Lecture Note Ser.},
number = {333},
url = {http://home.math.au.dk/kock/sdg99.pdf}}
@book{moerdijk:reyes:models,
author = {Moerdijk, I. and Reyes, G.},
title = {Models for Smooth Infinitesimal Analysis},
year = {1991},
publisher = {Springer}}
@inproceedings{mannaa:coquand:alg-closure,
author = {Mannaa, B. and Coquand, T.},
title = {A sheaf model of the algebraic closure},
booktitle = {Proc. of the Fifth International Workshop on Classical Logic and Computation},
year = {2014},
url = {https://arxiv.org/abs/1404.4549}}
@unpublished{pasquali:sheafification,
author = {Pasquali, F.},
title = {A sheafification theorem for doctrines},
year = {2014},
url = {https://arxiv.org/abs/1311.1424}}
@unpublished{henry:measure-theory-boolean-toposes,
author = {Henry, S.},
title = {Measure theory over boolean toposes},
year = {2014},
url = {https://arxiv.org/abs/1411.1605}}
@phdthesis{henry:classifying-topoi,
title = {Classifying topoi and preservation of higher order logic by geometric morphisms},
author = {Henry, S.},
year = {2013},
school = {University of Michigan},
url = {https://arxiv.org/abs/1305.3254}}
@book{borceux:handbook3,
author = {Borceux, F.},
title = {Handbook of Categorical Algebra: Volume 3, Sheaf Theory},
series = {Encyclopedia Math. Appl.},
year = {1994},
publisher = {Cambridge University Press}}
@inproceedings{birkedal:al:sgdt,
author = {Birkedal, L. and Mogelberg, R. and Schwinghammer, J. and Stovring, K.},
title = {First steps in synthetic guarded domain theory: step-indexing in the topos of trees},
year = {2012},
booktitle = {Proc. of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science},
url = {https://www.cs.au.dk/~birke/papers/sgdt-journal.pdf}}
@article{awodey-kishida:modal,
author = {Awodey, S. and Kishida, K.},
title = {Topology and modality: The topological interpretation of first-order modal logic},
year = {2008},
journal = {The Review of Symbolic Logic},
volume = {1, special issue 2},
pages = {146--166}}
@unpublished{caramello:1,
author = {Caramello, O.},
title = {The unification of mathematics via topos theory},
year = {2010},
url = {https://arxiv.org/abs/1006.3930}}
@unpublished{caramello:2,
author = {Caramello, O.},
title = {A topos-theoretic approach to Stone-type dualities},
year = {2011},
url = {https://arxiv.org/abs/1103.3493}}
@unpublished{caramello:lattices,
author = {Caramello, O.},
title = {Lattices of theories},
year = {2009},
url = {https://arxiv.org/abs/0905.0299}}
@unpublished{caramello:preliminaries,
author = {Caramello, O.},
title = {Topos-theoretic background},
year = {2014},
url = {https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf}}
@phdthesis{brandenburg:tensor-foundations,
author = {Brandenburg, M.},
title = {Tensor categorical foundations of algebraic geometry},
year = {2014},
school = {Universität Münster},
url = {https://arxiv.org/abs/1410.1716}}
@unpublished{brandenburg:schur,
author = {Brandenburg, M.},
title = {Operations on categories of modules are given by Schur functors},
year = {2016},
url = {https://arxiv.org/abs/1610.02180}}
@article{clr:dynamicalmethod,
author = {Coste, M. and Lombardi, H. and Roy, M.-F.},
title = {Dynamical method in algebra: ef{}fective Nullstellensätze},
journal = {Ann. Pure Appl. Logic},
volume = {111},
number = {3},
pages = {203--256},
year = {2001},
url = {https://perso.univ-rennes1.fr/michel.coste/publis/clr.pdf}}
@article{cl:logical,
author = {Coquand, T. and Lombardi, H.},
title = {A logical approach to abstract algebra},
journal = {Math. Structures Comput. Sci},
year = {2006},
volume = {16},
number = {5},
pages = {885--900},
url = {http://www.cse.chalmers.se/~coquand/FISCHBACHAU/AlgebraLogicCoqLom.pdf}}
@article{kock:univ-proj-geometry,
author = {Kock, A.},
title = {Universal projective geometry via topos theory},
journal = {J. Pure Appl. Algebra},
volume = {9},
number = {1},
pages = {1--24},
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