Professor
Ieke
Moerdijk
School of Mathematical and Physical Sciences
Chair
i.moerdijk@sheffield.ac.uk
Hicks Building
Full contact details
Professor Ieke Moerdijk
Hicks Building
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 additivity of the little cubes operads. Homology, Homotopy and Applications, 27(2), 171-179.
- On the equivalence of Lurie's ∞‐operads and dendroidal ∞-operads. Journal of Topology, 17(4). View this article in WRRO
- 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. Theory and Applications of Categories, 36, 118-170.
- An extension of Quillen’s Theorem B. Algebraic & Geometric Topology, 20(4), 1769-1794.
- Dendroidal spaces, $Γ$-spaces and the special Barratt-Priddy-Quillen theorem. Journal für die reine und angewandte Mathematik, 2020(760), 229-265. View this article in WRRO
- Exact completion of path categories and algebraic set theory: Part I: Exact completion of path categories. Journal of Pure and Applied Algebra, 222(10), 3137-3181. View this article in WRRO
- Univalent completion. Mathematische Annalen, 371(3-4), 1337-1350. View this article in WRRO
- Shuffles of trees. European Journal of Combinatorics , 71, 55-72. 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, 140-140.
- 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.
- On the equivalence between Lurie's model and the dendroidal model for
infinity-operads.
- 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.
- Derived rules for predicative set theory: An application of sheaves. Annals of Pure and Applied Logic, 163(10), 1367-1383.
- Dendroidal sets and simplicial operads.
- Aspects of predicative algebraic set theory, II: Realizability. Theoretical Computer Science, 412(20), 1916-1940.
- Dendroidal Segal spaces and infinity-operads.
- Derived rules for predicative set theory: an application of sheaves.
- ON THE UNIVERSAL ENVELOPING ALGEBRA OF A LIE ALGEBROID. P AM MATH SOC, 138(9), 3135-3145.
- 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 THE DERIVED CATEGORY OF AN ALGEBRA OVER AN OPERAD. GEORGIAN MATH J, 16(1), 13-28.
- On inner Kan complexes in the category of dendroidal sets. ADV MATH, 221(2), 343-389.
- Localization of algebras over coloured operads. Proceedings of the London Mathematical Society, 101(1), 105-136.
- Aspects of Predicative Algebraic Set Theory II: Realizability.
- On an extension of the notion of Reedy category. Math. Z. 269 (2011), 977-1004.
- Deformations of Lie brackets: cohomological aspects. J EUR MATH SOC, 10(4), 1037-1059.
- Aspects of Predicative Algebraic Set Theory I: Exact Completion.
- Dendroidal sets. ALGEBR GEOM TOPOL, 7, 1441-1470.
- On the developlability of Lie subalgebroids. ADV MATH, 210(1), 1-21.
- 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.
- Proper maps of toposes. Memoirs of the American Mathematical Society(711), 1-107.
- Foliation groupoids and their cyclic homology. ADV MATH, 157(2), 177-197.
- A homology theory for etale groupoids. J REINE ANGEW MATH, 521, 25-46.
- 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-+.
- 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.
- Simplicial cohomology of orbifolds. INDAGAT MATH NEW SER, 10(2), 269-293.
- Topological representation of sheaf cohomology of sites. COMPOS MATH, 118(2), 217-233.
- Representing topoi by topological groupoids. J PURE APPL ALGEBRA, 130(3), 223-235.
- Sets, Topoi and Intuitionism. Philosophia Mathematica, 6(2), 169-177.
- Proof of a conjecture of A. Haefliger. TOPOLOGY, 37(4), 735-741.
- Minimal models of Heyting arithmetic. J SYMBOLIC LOGIC, 62(4), 1448-1460.
- On the construction of the Grothendieck fundamental group of a topos by paths. J PURE APPL ALGEBRA, 116(1-3), 99-113.
- 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.
- Classifying spaces for toposes with enough points. Rendiconti Del Seminario Matematico E Fisico Di Milano, 66(1), 377-389.
- Topos theory, 1, 501-528.
- Spaces with local equivalence relations, and their monodromy. TOPOL APPL, 72(1), 47-78.
- 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 Remark on the Theory of Semi-Functors.. Math. Struct. Comput. Sci., 5, 1-8.
- 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 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.
- 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 ARE COHOMOLOGICALLY EQUIVALENT TO SPACES. AM J MATH, 112(1), 87-95.
- TOPOSES AS HOMOTOPY GROUPOIDS. ADV MATH, 80(1), 22-38.
- LOCAL-MAPS OF TOPOSES. P LOND MATH SOC, 58, 281-305.
- PRODISCRETE GROUPS AND GALOIS TOPOSES. P K NED AKAD A MATH, 92(2), 219-234.
- MORITA EQUIVALENCE FOR CONTINUOUS-GROUPS. MATH PROC CAMBRIDGE, 103, 97-115.
- TOPOSES AND GROUPOIDS. LECT NOTES MATH, 1348, 280-298.
- 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.
- FORCING SMOOTH SQUARE ROOTS AND INTEGRATION. FUND MATH, 128(3), 145-158.
- A SMOOTH VERSION OF THE ZARISKI TOPOS. ADV MATH, 65(3), 229-253.
- 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.
- 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.
- 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.
- DERHAM THEOREM IN A SMOOTH TOPOS. MATH PROC CAMBRIDGE, 96(JUL), 61-71.
- CONSTRUCTING CHOICE SEQUENCES FROM LAWLESS SEQUENCES OF NEIGHBORHOOD FUNCTIONS. LECT NOTES MATH, 1103, 207-234.
- SPACED SPACES. COMPOS MATH, 53(2), 171-209.
- SHEAF MODELS FOR CHOICE SEQUENCES. ANN PURE APPL LOGIC, 27(1), 63-107.
- SMOOTH SPACES VERSUS CONTINUOUS SPACES IN MODELS FOR SYNTHETIC DIFFERENTIAL GEOMETRY. J PURE APPL ALGEBRA, 32(2), 143-176.
- COMPOSITIONAL SEMANTICS AND MORPHOLOGICAL FEATURES. THEOR LINGUIST, 10(2-3), 205-225.
- EQUATIONAL CLASSES OF TOPOSES. COMMUN ALGEBRA, 11(8), 839-842.
- Some remarks on extending bar induction. Indagationes Mathematicae, 45(3), 315-318.
- On the Freyd cover of a topos.. Notre Dame Journal of Formal Logic, 24(4).
- 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.
- SOME TOPOLOGICAL-SPACES WHICH ARE UNIVERSAL FOR INTUITIONISTIC PREDICATE LOGIC. P K NED AKAD A MATH, 85(2), 227-235.
- 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.
- Homology of infinity-operads. Annales de l'Institut Fourier, 75(3), 929-965.
- Partition complexes and trees. Proceedings of the American Mathematical Society.
- The equivariant Serre spectral sequence. Proceedings of the American Mathematical Society, 118(1), 263-278.
- The classifying topos of a continuous groupoid. I. Transactions of the American Mathematical Society, 310(2), 629-668.
- Connected locally connected toposes are path-connected. Transactions of the American Mathematical Society, 295(2), 849-859.
Book chapters
- A small catalogue of (pp. 41-83). American Mathematical Society
- 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
- A Unified Approach to Algebraic Set Theory
- 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-+)
- Lie groupoids, gerbes, and non-Abelian cohomology. K-THEORY, Vol. 28(3) (pp 207-258)
- Preface (pp vii-x)
- 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)
Digital 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
- Koszul duality for algebras over infinity-operads, arXiv.
- 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.
- Left fibrations and homotopy colimits II, arXiv.
- Minimal fibrations of dendroidal sets, arXiv.
- Univalent completion, arXiv.
- Note on the tensor product of dendroidal sets.
- 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.
- Simplicial and Dendroidal Homotopy Theory. Springer International Publishing.
- Research group
- Grants
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Past Grants, as Coinvestigator Workshop on Lie Algebroids and Lie Groupoids in Differential Geometry EPSRC