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
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Books
- . Springer International Publishing.
- . Springer International Publishing.
- . Springer Basel.
- . Cambridge University Press.
- . Cambridge University Press.
- . Springer Berlin Heidelberg.
- . Springer New York.
- . Springer New York.
Journal articles
- . Journal of Topology, 17(4).
- . Algebraic & Geometric Topology, 23(8), 3849-3908.
- . Advances in Mathematics, 408, 108601-108601.
- Closed dendroidal sets and unital operads. Theory and Applications of Categories, 36, 118-170.
- 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.
- . Theory and Applications of Categories, 36, 118-170.
- . Algebraic & Geometric Topology, 20(4), 1769-1794.
- . Journal für die reine und angewandte Mathematik, 2020(760), 229-265.
- . Journal of Pure and Applied Algebra, 222(10), 3137-3181.
- . Mathematische Annalen, 371(3-4), 1337-1350.
- . European Journal of Combinatorics , 71, 55-72.
- . Mathematical Proceedings of the Cambridge Philosophical Society.
- W-types in homotopy-type theory - CORRIGENDUM.. Mathematical Structures in Computer Science, 28, 140-140.
- . Algebraic & Geometric Topology, 16(6), 3581-3614.
- . Notices of the American Mathematical Society, 62(09), 1042-1042.
- . 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.
- . Annals of Pure and Applied Logic, 163(10), 1367-1383.
- Dendroidal sets and simplicial operads.
- . 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.
- . 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.
- . ALGEBR GEOM TOPOL, 7, 1441-1470.
- . ADV MATH, 210(1), 1-21.
- . TOPOLOGY, 45(5), 807-849.
- . ADV MATH, 204(1), 101-115.
- Families of Hopf algebras of trees and pre-Lie algebras. HOMOL HOMOTOPY APPL, 8(1), 243-256.
- . MATH ANN, 328(1-2), 59-85.
- . 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.
- . 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-+.
- . 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.
- . 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.
- . Rendiconti Del Seminario Matematico E Fisico Di Milano, 66(1), 377-389.
- , 1, 501-528.
- Spaces with local equivalence relations, and their monodromy. TOPOL APPL, 72(1), 47-78.
- . Journal of Symbolic Logic, 60(2), 694-695.
- . 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.
- . 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.
- . 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.
- . 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.
- . Studies in Logic and the Foundations of Mathematics, 110(C), 275-295.
- . Studies in Logic and the Foundations of Mathematics, 110(C), 359-375.
- . Annales de l'Institut Fourier, 75(3), 929-965.
- . Proceedings of the American Mathematical Society.
- . Proceedings of the American Mathematical Society, 118(1), 263-278.
- . Transactions of the American Mathematical Society, 310(2), 629-668.
- . Transactions of the American Mathematical Society, 295(2), 849-859.
Book chapters
- , Lecture Notes in Mathematics (pp. 209-214). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 353-420). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 133-160). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 49-90). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 555-590). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 423-451). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 3-48). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 303-352). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 265-301). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 161-210). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 211-261). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 481-521). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 91-131). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 453-480). Springer International Publishing
- , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (pp. 523-553). Springer International Publishing
- , European Congress of Mathematics (pp. 481-489). Birkhäuser Basel
- (pp. 101-114). American Mathematical Society
- , Handbook of Algebra (pp. xix-xix). Elsevier
- , Mathematical Sciences Research Institute Publications (pp. 373-385). Springer New York
- , Algebraic K-Theory: Connections with Geometry and Topology (pp. 225-240). Springer Netherlands
- , 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)
- (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
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- Note on the tensor product of dendroidal sets.
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