paper-flabby-objects.bib

@inproceedings{kock:partial-maps,
  author = {Kock, A.},
  title = {Algebras for the partial map classifier monad},
  editor = {Carboni, A. and Pedicchio, M. and Rosolini, G.},
  booktitle = {Category Theory. Proceedings of the International Conference held in Como, Italy, July 22–28, 1990},
  publisher = {Springer},
  year = {1991},
  series = {Lecture Notes in Math.},
  volume = {1488},
  pages = {262--278}}

@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{blass:inj-proj-axc,
  author = {Blass, A.},
  title = {Injectivity, projectivity, and the axiom of choice},
  year = {1979},
  journal = {Trans. Amer. Math. Soc.},
  volume = {255},
  pages = {31--59}}

@unpublished{shulman:stack-semantics,
  author = {Shulman, M.},
  title = {Stack semantics and the comparison of material and structural set theories},
  year = {2010},
  url = {https://arxiv.org/abs/1004.3802}}

@article{harting:locally-injective,
  author = {Harting, R.},
  title = {Locally injective abelian groups in a topos},
  year = {1983},
  journal = {Comm. Algebra},
  volume = {11},
  number = {4},
  pages = {349--376}}

@article{harting:remark,
  author = {Harting, R.},
  title = {A remark on injectivity of sheaves of abelian groups},
  year = {1981},
  journal = {Archiv der Mathematik},
  volume = {36},
  number = {1},
  pages = {230--233}}

@article{harting:coproduct,
  author = {Harting, R.},
  title = {Internal coproduct of abelian groups in an elementary topos},
  journal = {Comm. Algebra},
  volume = {10},
  number = {11},
  pages = {1173--1237},
  year = {1982}}

@article{harting:effacements,
  author = {Harting, R.},
  title = {Abelian groups in a topos: injectives and injective effacements},
  journal = {J. Pure Appl. Algebra},
  volume = {30},
  year = {1983},
  pages = {247--260}}

@inproceedings{hyland:effective-topos,
  author = {Hyland, M.},
  title = {The ef{}fective topos},
  editor = {Troelstra, A. S. and van Dalen, D.},
  booktitle = {The L. E. J. Brouwer Centenary Symposium},
  publisher = {North-Holland},
  year = {1982},
  pages = {165--216}}

@inproceedings{altenkirch-kaposi:qits,
  author = {Altenkirch, T. and Kaposi, A.},
  title = {Type theory in type theory using quotient inductive types},
  booktitle = {Proceedings of POPL '16},
  publisher = {ACM},
  pages = {18--29},
  year = {2016}}

@article{moerdijk-palmgren:wellfounded-trees,
  author = {Moerdijk, I. and Palmgren, E.},
  title = {Wellfounded trees in categories},
  journal = {Ann. Pure Appl. Logic},
  volume = {104},
  year = {2000},
  pages = {189--218}}

@misc{berg-moerdijk:w-types-in-sheaves,
  author = {van den Berg, B. and Moerdijk, I.},
  title = {$W$-types in sheaves},
  url = {https://arxiv.org/abs/0810.2398},
  year = {2008}}

@misc{berg-kouwenhoven-gentil:w-types-in-eff,
  author = {van den Berg, B. and Kouwenhoven-Gentil, C.},
  title = {$W$-types in the ef{}fective topos},
  url = {https://www.staff.science.uu.nl/~ooste110/realizability/WinEff.ps.gz},
  year = {2004}}

@misc{shulman-lumsdaine:hits,
  author = {Shulman, M. and Lumsdaine, P.},
  title = {Semantics of higher inductive types},
  url = {https://arxiv.org/abs/1705.07088},
  year = {2017}}

@article{blass:free-algebras,
  author = {Blass, A.},
  title = {Words, free algebras, and coequalizers},
  journal = {Fund. Math.},
  volume = {117},
  number = {2},
  pages = {117--160},
  year = {1983}}

@article{aczel-berg-granstroem-schuster:injective,
  title = {Are there enough injective sets?},
  author = {Aczel, P. and van den Berg, B. and Granstroem, J. and Schuster, P.},
  year = {2013},
  journal = {Studia Logica},
  volume = {101},
  number = {3},
  pages = {467--482}}

@article{kenney:injective-choice,
  author = {Kenney, T.},
  title = {Injective power objects and the axiom of choice},
  journal = {J. Pure Appl. Algebra},
  volume = {215},
  issue = {2},
  year = {2011},
  pages = {131--144}}

@article{bauer:injection,
  author = {Bauer, A.},
  title = {An injection from the Baire space to natural numbers},
  journal = {Math. Structures Comput. Sci.},
  volume = {25},
  number = {7},
  pages = {1484--1489},
  year = {2015}}

@article{hamkins-lewis:ittm,
  title = {Infinite time Turing machines},
  author = {Hamkins, J. and Lewis, A.},
  journal = {J. Symbolic Logic},
  volume = {65},
  number = {2},
  year = {2000},
  pages = {567--604}}

@mastersthesis{blechschmidt:master,
  title = {Topostheorie und algebraische Geometrie},
  author = {Blechschmidt, I.},
  school = {University of Augsburg},
  year = {2012},
  url = {https://www.ingo-blechschmidt.eu/masters-thesis.pdf}}

@book{johnstone:elephant,
  author = {Johnstone, P. T.},
  title = {Sketches of an Elephant: A Topos Theory Compendium},
  year = {2002},
  publisher = {Oxford University Press}}

@phdthesis{blechschmidt:phd,
  author = {Blechschmidt, I.},
  title = {Using the internal language of toposes in algebraic geometry},
  year = {2017},
  school = {University of Augsburg},
  url = {https://rawgit.com/iblech/internal-methods/master/notes.pdf}}

@misc{blechschmidt:generic-freeness,
  author = {Blechschmidt, I.},
  title = {An elementary and constructive proof of Grothendieck's generic freeness lemma},
  year = {2018},
  url = {https://arxiv.org/abs/1807.01231}}

@book{hott,
  author = {The {Univalent Foundations Program}},
  title  = {Homotopy Type Theory: Univalent Foundations of Mathematics},
  url = {https://homotopytypetheory.org/book},
  address = {Institute for Advanced Study},
  year = {2013}}

@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{goldblatt:topoi,
  author = {Goldblatt, R.},
  title = {Topoi: The Categorical Analysis of Logic},
  year = {1984},
  publisher = {Elsevier},
  series = {Stud. Logic Found. Math.},
  volume = {98}}

@book{caramello:ttt,
  author = {Caramello, O.},
  title = {Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic `bridges'},
  publisher = {Oxford University Press},
  year = {2018}}

@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}}

@article{barakat-lh:ext,
  author = {Barakat, M. and Lange-Hegermann, M.},
  title = {On the Ext-computability of Serre quotient categories},
  journal = {J. Algebra},
  volume = {240},
  year = {2014},
  pages = {333--349}}

@article{barakat-lh:homalg,
  author = {Barakat, M. and Lange-Hegermann, M.},
  title = {An axiomatic setup for algorithmic homological algebra and an alternative approach to localization},
  journal = {J. Algebra Appl.},
  volume = {10},
  number = {2},
  year = {2011},
  pages = {269--293}}

@techreport{phoa:effective,
  author = {Phoa, W.},
  title = {An introduction to fibrations, topos theory, the ef{}fective topos and modest sets},
  institution = {University of Edinburgh},
  year = {1992},
  note = {\url{http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208/}}}

@misc{bauer:c2c,
  author = {Bauer, A.},
  title = {Realizability as the connection between computable and constructive mathematics},
  year = {2005},
  note = {\url{http://math.andrej.com/asset/data/c2c.pdf}}}

@book{oosten:realizability,
  author = {van Oosten, J.},
  title = {Realizability: An Introduction to its Categorical Side},
  year = {2008},
  series = {Stud. Logic Found. Math.},
  volume = {152},
  publisher = {Elsevier}}

@misc{moerdijk-oosten:topos-theory,
  author = {Moerdijk, I. and van Oosten, J.},
  title = {Topos theory},
  year = {2007},
  note = {Lecture notes},
  url = {https://webspace.science.uu.nl/~ooste110/syllabi/toposmoeder.pdf}}

@article{kempf:cohomology,
  author = {Kempf, G.},
  title = {Some elementary proofs of basic theorems in the cohomology of quasi-coherent sheaves},
  journal = {Rocky Mountain J. Math.},
  volume = {10},
  number = {3},
  year = {1980},
  pages = {637--646}}

@misc{stacks-project,
  author = "The {Stacks Project Authors}",
  title = "{Stacks Project}",
  url = {https://stacks.math.columbia.edu/}}

@article{johnstone:review-oosten,
  author = {Johnstone, P.},
  title = {{Jaap van Oosten. Realizability: an introduction to its categorical side. Studies in Logic and the Foundations of Mathematics [book review]}},
  year = {2010},
  journal = {Bull. Symbolic Logic},
  volume = {16},
  number = {3},
  pages = {407--409}}

@inproceedings{fourman-scott:sheaves-and-logic,
  author = {Fourman, M. and Scott, D.},
  title = {Notes on sheaves and logic},
  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}}

@article{goldblatt:modality,
  author = {Goldblatt, R.},
  title = {Grothendieck topology as geometric modality},
  year = {1981},
  journal = {MLQ Math. Log. Q.},
  volume = {27},
  number = {31--35},
  pages = {495--529}}

@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}}

@incollection{crosilla:cst-izf,
  author = {Crosilla, L.},
  title  = {Set theory: constructive and intuitionistic {ZF}},
  booktitle = {The Stanford Encyclopedia of Philosophy},
  editor = {Zalta, E.},
  url = {https://plato.stanford.edu/archives/sum2015/entries/set-theory-constructive/},
  year = {2015},
  publisher = {Metaphysics Research Lab, Stanford University}}

@incollection{crosilla:predicativity,
  author = {Crosilla, L.},
  title = {Exploring predicativity},
  booktitle = {Proof and Computation},
  editor = {Mainzer, K. and Schuster, P. and Schwichtenberg, H.},
  publisher = {World Scientific},
  year = {2018},
  pages = {83--108}}

@article{maietti:au,
  author = {Maietti, M.},
  title = {Joyal's arithmetic universes as list-arithmetic pretoposes},
  year = {2010},
  journal = {Theory Appl. Categ.},
  volume = {23},
  number = {3},
  pages = {39--83}}

@article{vickers:sketches,
  author = {Vickers, S.},
  title = {Sketches for arithmetic universes},
  year = {2016},
  journal = {J. Log. Anal.},
  volume = {11},
  pages = {1--56},
  number = {FT4}}

@article{maietti-vickers:induction,
  author = {Maietti, M. and Vickers, S.},
  title = {An induction principle for consequence in arithmetic universes},
  journal = {J. Pure Appl. Algebra},
  volume = {216},
  number = {8--9},
  year = {2012},
  pages = {2049--2067}}

@article{maietti:modular,
  author = {Maietti, M.},
  title = {Modular correspondence between dependent type theories and categories including pretopoi and topoi},
  journal = {Math. Structures Comput. Sci.},
  volume = {15},
  number = {6},
  year = {2005},
  pages = {1089--1149}}

@article{vickers:classifying,
  author = {Vickers, S.},
  title = {Arithmetic universes and classifying toposes},
  year = {2017},
  journal = {Cah. Topol. Géom. Différ. Catég.},
  volume = {58},
  number = {4},
  pages = {213--248}}

@phdthesis{hazratpour:phd,
  author = {Hazratpour, S.},
  title = {A logical study of some 2-categorical aspects of topos theory},
  year = {2019},
  school = {University of Birmingham},
  url = {https://etheses.bham.ac.uk/id/eprint/9752/7/Hazratpour2019PhD.pdf}}

@book{riehl:cathtpy,
  author = {Riehl, E.},
  title = {Categorical homotopy theory},
  year = {2014},
  publisher = {Cambridge University Press},
  series = {New Math. Monogr.}}

@article{tenorio-mariano:cohomology,
  author = {Tenorio, A. and Mariano, H.},
  title = {On sheaf cohomology and natural expansions},
  journal = {São Paulo J. Math. Sci.},
  volume = {15},
  number = {2},
  year = {2021},
  pages = {571--614}}

@article{huang:cohomology,
  title = {Cohomology of projective space seen by residual complex},
  author = {Huang, I-C.},
  journal = {Trans. Amer. Math. Soc.},
  volume = {353},
  number = {8},
  pages = {3097--3114}}

@article{hinich:what-is,
  title = {So, what is a derived functor?},
  author = {Hinich, V.},
  journal = {Homology, Homotopy Appl.},
  volume = {22},
  number = {2},
  year = {2020},
  pages = {279--293}}

@article{maltsiniotis:adjunction,
  title = {Le théorème de Quillen, d’adjonction des foncteurs dérivés, revisité},
  author = {Maltsiniotis, G.},
  journal = {C. R. Acad. Sci. Paris, Ser. I},
  volume = {344},
  year = {2007},
  pages = {549-–552}}