Professor Izak Moerdijk
School of Mathematical and Physical Sciences
Chair
i.moerdijk@sheffield.ac.uk
Hicks Building
Full contact details
Professor Izak Moerdijk
School of Mathematical and Physical Sciences
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematical and Physical Sciences
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Publications
-
Books
- Simplicial and Dendroidal Homotopy Theory. Springer International Publishing.
- Sets, Models and Proofs. Springer International Publishing.
- Simplicial Methods for Operads and Algebraic Geometry. Springer Basel.
- Introduction to Foliations and Lie Groupoids. Cambridge University Press.
- Algebraic Set Theory. Cambridge University Press.
- Classifying Spaces and Classifying Topoi. Springer Berlin Heidelberg.
- Sheaves in Geometry and Logic. Springer New York.
- Models for Smooth Infinitesimal Analysis. Springer New York.
Journal articles
- On the equivalence of Lurie's ∞$infty$‐operads and dendroidal ∞$infty$‐operads. Journal of Topology, 17(4).
- Simplicial model structures on pro-categories. Algebraic & Geometric Topology, 23(8), 3849-3908.
- Profinite ∞-operads. Advances in Mathematics, 408, 108601-108601.
- CLOSED DENDROIDAL SETS AND UNITAL OPERADS To Bob Rosebrugh, in gratitude for all his work for the journal. THEORY AND APPLICATIONS OF CATEGORIES, 36, 118-170.
- Closed dendroidal sets and unital operads. Theory and Applications of Categories, 36, 118-170.
- An extension of Quillen’s Theorem B. Algebraic & Geometric Topology, 20(4), 1769-1794.
- Shuffles of trees. European Journal of Combinatorics, 71, 55-72. View this article in WRRO
- Dendroidal spaces, Γ-spaces and the special Barratt--Priddy--Quillen theorem. Journal für die reine und angewandte Mathematik (Crelles Journal). View this article in WRRO
- The dendroidal category is a test category. Mathematical Proceedings of the Cambridge Philosophical Society.
- W-types in homotopy-type theory – CORRIGENDUM. Mathematical Structures in Computer Science, 28(1), 140-140.
- Exact completion of path categories and algebraic set theory: Part I: Exact completion of path categories. Journal of Pure and Applied Algebra. View this article in WRRO
- Univalent completion. Mathematische Annalen. View this article in WRRO
- Minimal fibrations of dendroidal sets. Algebraic & Geometric Topology, 16(6), 3581-3614. View this article in WRRO
- Daniel M. Kan (1927—2013). Notices of the American Mathematical Society, 62(09), 1042-1042.
- Left fibrations and homotopy colimits. Mathematische Zeitschrift, 279(3-4), 723-744.
- Derived rules for predicative set theory: An application of sheaves. Annals of Pure and Applied Logic, 163(10), 1367-1383.
- Aspects of predicative algebraic set theory, II: Realizability. Theoretical Computer Science, 412(20), 1916-1940.
- ON THE UNIVERSAL ENVELOPING ALGEBRA OF A LIE ALGEBROID. P AM MATH SOC, 138(9), 3135-3145.
- On inner Kan complexes in the category of dendroidal sets. ADV MATH, 221(2), 343-389.
- ON THE DERIVED CATEGORY OF AN ALGEBRA OVER AN OPERAD. GEORGIAN MATH J, 16(1), 13-28.
- Deformations of Lie brackets: cohomological aspects. J EUR MATH SOC, 10(4), 1037-1059.
- On the developlability of Lie subalgebroids. ADV MATH, 210(1), 1-21.
- Dendroidal sets. ALGEBR GEOM TOPOL, 7, 1441-1470.
- The Boardman-Vogt resolution of operads in monoidal model categories. TOPOLOGY, 45(5), 807-849.
- On the integrability of Lie subalgebroids. ADV MATH, 204(1), 101-115.
- Families of Hopf algebras of trees and pre-Lie algebras. HOMOL HOMOTOPY APPL, 8(1), 243-256.
- Cech-De Rham theory for leaf spaces of foliations. MATH ANN, 328(1-2), 59-85.
- Axiomatic homotopy theory for operads. COMMENT MATH HELV, 78(4), 805-831.
- On integrability of infinitesimal actions. AM J MATH, 124(3), 567-593.
- Foliation groupoids and their cyclic homology. ADV MATH, 157(2), 177-197.
- Proper maps of toposes. Memoirs of the American Mathematical Society(711), 1-107.
- Category theory and its applications - Preface. J PURE APPL ALGEBRA, 154(1-3), 1-1.
- Proper maps of toposes. MEM AM MATH SOC, 148(705), 1-+.
- A homology theory for etale groupoids. J REINE ANGEW MATH, 521, 25-46.
- Proper maps of toposes. Memoirs of the American Mathematical Society, 148(705).
- An elementary definability theorem for first order logic. J SYMBOLIC LOGIC, 64(3), 1028-1036.
- Topological representation of sheaf cohomology of sites. COMPOS MATH, 118(2), 217-233.
- Simplicial cohomology of orbifolds. INDAGAT MATH NEW SER, 10(2), 269-293. View this article in WRRO
- Representing topoi by topological groupoids. J PURE APPL ALGEBRA, 130(3), 223-235.
- Proof of a conjecture of A. Haefliger. TOPOLOGY, 37(4), 735-741.
- Sets, Topoi and Intuitionism. Philosophia Mathematica, 6(2), 169-177.
- Minimal models of Heyting arithmetic. J SYMBOLIC LOGIC, 62(4), 1448-1460.
- Representation of topoi by topological spaces. CR ACAD SCI I-MATH, 325(5), 461-464.
- Path-lifting for Grothendieck toposes (vol 102, pg 241, 1988). P AM MATH SOC, 125(9), 2815-2818.
- Orbifolds, sheaves and groupoids. K-THEORY, 12(1), 3-21.
- On the construction of the Grothendieck fundamental group of a topos by paths. J PURE APPL ALGEBRA, 116(1-3), 99-113.
- Spaces with local equivalence relations, and their monodromy. TOPOL APPL, 72(1), 47-78.
- Classifying spaces for toposes with enough points. Rendiconti del Seminario Matematico e Fisico di Milano, 66(1), 377-389.
- Topos theory, 1, 501-528.
- Jonahan Chapman and Frederick Rowbottom. Relative category theory and geometric morphisms. A logical approach. Oxford logic guides, no. 16., Clarendon press, Oxford University Press, Oxford and New York1992, xi + 263 pp.. Journal of Symbolic Logic, 60(2), 694-695.
- A MODEL FOR INTUITIONISTIC NONSTANDARD ARITHMETIC. ANN PURE APPL LOGIC, 73(1), 37-51.
- A SHAPIRO LEMMA FOR DIAGRAMS OF SPACES WITH APPLICATIONS TO EQUIVARIANT TOPOLOGY. COMPOS MATH, 96(3), 249-282.
- A Remark on the Theory of Semi-Functors.. Math. Struct. Comput. Sci., 5, 1-8.
- A COMPLETENESS THEOREM FOR OPEN MAPS. ANN PURE APPL LOGIC, 70(1), 51-86.
- ALGEBRAIC CLASSIFICATION OF EQUIVARIANT HOMOTOPY 2-TYPES .1.. J PURE APPL ALGEBRA, 89(1-2), 187-216.
- CLASSIFYING-SPACES, CLASSIFYING TOPOI AND AUGMENTED ORDERS. CR ACAD SCI I-MATH, 317(3), 293-298.
- THE EQUIVARIANT SERRE SPECTRAL SEQUENCE. P AM MATH SOC, 118(1), 263-278.
- The equivariant Serre spectral sequence. Proceedings of the American Mathematical Society, 118(1), 263-263.
- EVERY ETENDUE COMES FROM A LOCAL EQUIVALENCE RELATION. J PURE APPL ALGEBRA, 82(2), 155-174.
- CLASSIFYING TOPOSES AND FOLIATIONS. ANN I FOURIER, 41(1), 189-209.
- Book Review: Mathematical intuitionism. Introduction to proof theory. Bulletin of the American Mathematical Society, 22(2), 301-305.
- TOPOSES AS HOMOTOPY GROUPOIDS. ADV MATH, 80(1), 22-38.
- TOPOSES ARE COHOMOLOGICALLY EQUIVALENT TO SPACES. AM J MATH, 112(1), 87-95.
- PRODISCRETE GROUPS AND GALOIS TOPOSES. P K NED AKAD A MATH, 92(2), 219-234.
- LOCAL-MAPS OF TOPOSES. P LOND MATH SOC, 58, 281-305.
- THE CLASSIFYING TOPOS OF A CONTINUOUS GROUPOID .1.. T AM MATH SOC, 310(2), 629-668.
- PATH-LIFTING FOR GROTHENDIECK TOPOSES. P AM MATH SOC, 102(2), 242-248.
- TOPOSES AND GROUPOIDS. LECT NOTES MATH, 1348, 280-298.
- MORITA EQUIVALENCE FOR CONTINUOUS-GROUPS. MATH PROC CAMBRIDGE, 103, 97-115.
- A SMOOTH VERSION OF THE ZARISKI TOPOS. ADV MATH, 65(3), 229-253.
- FORCING SMOOTH SQUARE ROOTS AND INTEGRATION. FUND MATH, 128(3), 145-158.
- CONNECTED LOCALLY CONNECTED TOPOSES ARE PATH-CONNECTED. T AM MATH SOC, 295(2), 849-859.
- RINGS OF SMOOTH FUNCTIONS AND THEIR LOCALIZATIONS .1.. J ALGEBRA, 99(2), 324-336.
- Connected locally connected toposes are path-connected. Transactions of the American Mathematical Society, 295(2), 849-849.
- CONTINUOUS FIBRATIONS AND INVERSE LIMITS OF TOPOSES. COMPOS MATH, 58(1), 45-72.
- An elementary proof of the descent theorem for Grothendieck toposes. Journal of Pure and Applied Algebra, 37(C), 185-191.
- SPACED SPACES. COMPOS MATH, 53(2), 171-209.
- CONSTRUCTING CHOICE SEQUENCES FROM LAWLESS SEQUENCES OF NEIGHBORHOOD FUNCTIONS. LECT NOTES MATH, 1103, 207-234.
- SHEAF MODELS FOR CHOICE SEQUENCES. ANN PURE APPL LOGIC, 27(1), 63-107.
- DERHAM THEOREM IN A SMOOTH TOPOS. MATH PROC CAMBRIDGE, 96(JUL), 61-71.
- SMOOTH SPACES VERSUS CONTINUOUS SPACES IN MODELS FOR SYNTHETIC DIFFERENTIAL GEOMETRY. J PURE APPL ALGEBRA, 32(2), 143-176.
- ON CHOICE SEQUENCES DETERMINED BY SPREADS. J SYMBOLIC LOGIC, 49(3), 908-916.
- HEINE-BOREL DOES NOT IMPLY THE FAN THEOREM. J SYMBOLIC LOGIC, 49(2), 514-519.
- On the Freyd cover of a topos.. Notre Dame Journal of Formal Logic, 24(4), 517-526.
- Some remarks on extending bar induction. Indagationes Mathematicae, 45(3), 315-318.
- COMPOSITIONAL SEMANTICS AND MORPHOLOGICAL FEATURES. THEOR LINGUIST, 10(2-3), 205-225.
- COMPOSITIONALITY AND THE ANALYSIS OF ANAPHORA. LINGUIST PHILOS, 6(1), 89-114.
- SOME REMARKS ON EXTENDING BAR INDUCTION. P K NED AKAD A MATH, 86(3), 315-318.
- EQUATIONAL CLASSES OF TOPOSES. COMMUN ALGEBRA, 11(8), 839-842.
- Two sheaf representations of elementary toposes. Studies in Logic and the Foundations of Mathematics, 110(C), 275-295.
- Glueing topoi and higher order disjunction and existence. Studies in Logic and the Foundations of Mathematics, 110(C), 359-375.
- SOME TOPOLOGICAL-SPACES WHICH ARE UNIVERSAL FOR INTUITIONISTIC PREDICATE LOGIC. P K NED AKAD A MATH, 85(2), 227-235.
- Homology of infinity-operads. Annales de l'Institut Fourier, 1-37.
- Partition complexes and trees. Proceedings of the American Mathematical Society.
- On the equivalence between Lurie's model and the dendroidal model for
infinity-operads. View this article in WRRO
- W-types in Homotopy Type Theory.
- The Axiom of Multiple Choice and Models for Constructive Set Theory.
- On the homotopy theory of enriched categories. Quart. J. Math. 64 (2013), 805-846.
- Dendroidal sets and simplicial operads.
- Dendroidal Segal spaces and infinity-operads.
- Derived rules for predicative set theory: an application of sheaves.
- Aspects of Predicative Algebraic Set Theory III: Sheaves.
- Dendroidal sets as models for homotopy operads. Journal of Topology 4 (2011), no. 2, 257-299.
- On an extension of the notion of Reedy category. Math. Z. 269 (2011), 977-1004.
- Localization of algebras over coloured operads. Proceedings of the London Mathematical Society, 101(1), 105-136.
- Aspects of Predicative Algebraic Set Theory II: Realizability.
- Aspects of Predicative Algebraic Set Theory I: Exact Completion.
- The classifying topos of a continuous groupoid. I. Transactions of the American Mathematical Society, 310(2), 629-668.
- Closed dendroidal sets and unital operads.
Chapters
- A Mysterious Tensor Product in Topology, Lecture Notes in Mathematics (pp. 209-214). Springer International Publishing
- Three Model Structures on the Category of Dendroidal Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 353-420). Springer International Publishing
- Tensor Products of Dendroidal Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 133-160). Springer International Publishing
- Simplicial Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 49-90). Springer International Publishing
- Simplicial Operads and ∞-Operads, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 555-590). Springer International Publishing
- Reedy Categories and Diagrams of Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 423-451). Springer International Publishing
- Operads, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 3-48). Springer International Publishing
- Model Structures on the Category of Simplicial Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 303-352). Springer International Publishing
- Model Categories, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 265-301). Springer International Publishing
- Kan Conditions for Simplicial Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 161-210). Springer International Publishing
- Kan Conditions for Dendroidal Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 211-261). Springer International Publishing
- Dendroidal Spaces and ∞-Operads, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 481-521). Springer International Publishing
- Dendroidal Sets, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 91-131). Springer International Publishing
- Mapping Spaces and Bousfield Localizations, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 453-480). Springer International Publishing
- Left Fibrations and the Covariant Model, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 523-553). Springer International Publishing
- Models for the Leaf Space of a Foliation, European Congress of Mathematics (pp. 481-489). Birkhäuser Basel
- Étale groupoids, derived categories, and operations (pp. 101-114). American Mathematical Society
- List of Contributors, Handbook of Algebra (pp. xix-xix). Elsevier
- Reals and Forcing with an Elementary Topos, Mathematical Sciences Research Institute Publications (pp. 373-385). Springer New York
- Bisimplicial Sets and the Group-Completion Theorem, Algebraic K-Theory: Connections with Geometry and Topology (pp. 225-240). Springer Netherlands
- Two Sheaf Representations of Elementary Toposes., Studies in Logic and the Foundations of Mathematics (pp. 275-295). Elsevier
Conference proceedings papers
- Resolution of coloured operads and rectification of homotopy algebras. Categories in Algebra, Geometry and Mathematical Physics, Vol. 431 (pp 31-58)
- Lie groupoids, sheaves and cohomology. Poisson Geometry, Deformation Quantisation and Group Representations, Vol. 323 (pp 145-+)
- Preface (pp vii-x)
- Lie groupoids, gerbes, and non-Abelian cohomology. K-THEORY, Vol. 28(3) (pp 207-258)
- Type theories, toposes and constructive set theory: predicative aspects of AST. ANNALS OF PURE AND APPLIED LOGIC, Vol. 114(1-3) (pp 155-201)
- Monads on tensor categories. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 168(2-3) (pp 189-208)
- Wellfounded trees in categories. ANNALS OF PURE AND APPLIED LOGIC, Vol. 104(1-3) (pp 189-218)
- Proof of a conjecture of A. Pitts. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 143(1-3) (pp 329-338)
- On the weak homotopy type of Etale groupoids. INTEGRABLE SYSTEMS AND FOLIATIONS, Vol. 145 (pp 147-156)
- A Unified Approach to Algebraic Set Theory
Website content
- Home Page.
Working papers
- W-types in sheaves.
- On the universal enveloping algebra of a Lie-Rinehart algebra. published as: On the universal enveloping algebra of a Lie
algebroid. Proc. Amer. Math. Soc., 138, 3135-3145.
- Introduction to the language of stacks and gerbes.
- The renormalisation bialgebra and operads.
- Orbifolds as Groupoids: an Introduction.
- On the Classification of Regular Groupoids.
- On the Connes-Kreimer construction of Hopf Algebras.
- A definability theorem for first order logic.
Preprints
- Addendum: localization of lax symmetric monoidal categories, arXiv.
- Profinite completions of topological operads, arXiv.
- A small catalogue of En-operads, arXiv.
- On the equivalence of the Lurie's $infty$-operads and dendroidal $infty$-operads, arXiv.
- On the additivity of the little cubes operads, arXiv.
- Partition complexes and trees, arXiv.
- Profinite $infty$-operads, arXiv.
- Homology of infinity-operads, arXiv.
- Simplicial model structures on pro-categories, arXiv.
- Closed dendroidal sets and unital operads, arXiv.
- An extension of Quillen's Theorem B, arXiv.
- Shuffles of trees, arXiv.
- The dendroidal category is a test category, arXiv.
- Dendroidal spaces, $Gamma$-spaces and the special Barratt-Priddy-Quillen theorem, arXiv.
- Exact completion of path categories and algebraic set theory -- Part I: Exact completion of path categories, arXiv.
- Minimal fibrations of dendroidal sets, arXiv.
- Univalent completion, arXiv.
- Left fibrations and homotopy colimits, arXiv.
- W-types in Homotopy Type Theory, arXiv.
- On the equivalence between Lurie's model and the dendroidal model for infinity-operads, arXiv.
- The Axiom of Multiple Choice and Models for Constructive Set Theory, arXiv.
- On the homotopy theory of enriched categories, arXiv.
- Dendroidal sets and simplicial operads, arXiv.
- Dendroidal Segal spaces and infinity-operads, arXiv.
- Derived rules for predicative set theory: an application of sheaves, arXiv.
- Aspects of Predicative Algebraic Set Theory III: Sheaves, arXiv.
- Dendroidal sets as models for homotopy operads, arXiv.
- On an extension of the notion of Reedy category, arXiv.
- Localization of algebras over coloured operads, arXiv.
- On the derived category of an algebra over an operad, arXiv.
- Aspects of Predicative Algebraic Set Theory II: Realizability, arXiv.
- Aspects of Predicative Algebraic Set Theory I: Exact Completion, arXiv.
- A Unified Approach to Algebraic Set Theory, arXiv.
- Dendroidal Sets, arXiv.
- On inner Kan complexes in the category of dendroidal sets, arXiv.
- Resolution of coloured operads and rectification of homotopy algebras, arXiv.
- The Boardman-Vogt resolution of operads in monoidal model categories, arXiv.
- On the developability of subalgebroids, arXiv.
- On the integrability of subalgebroids, arXiv.
- Deformations of Lie brackets: cohomological aspects, arXiv.
- Families of Hopf algebras of trees and pre-Lie algebras, arXiv.
- Axiomatic homotopy theory for operads, arXiv.
- Orbifolds as Groupoids: an Introduction, arXiv.
- Cech-De Rham theory for leaf spaces of foliations, arXiv.
- On integrability of infinitesimal actions, arXiv.
- Foliation groupoids and their cyclic homology, arXiv.
- On the Connes-Kreimer construction of Hopf Algebras, arXiv.
- A Homology Theory for Etale Groupoids, arXiv.
- simplicial cohomology of orbifolds, arXiv.
- A definability theorem for first order logic, arXiv.
- Left fibrations and homotopy colimits.
- Note on the tensor product of dendroidal sets.
- Simplicial and Dendroidal Homotopy Theory. Springer International Publishing.