Moerdijk, Ieke
Overview
Works:  119 works in 285 publications in 3 languages and 5,295 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Other, Editor, Thesis advisor, 956, Opponent, htt 
Publication Timeline
.
Most widely held works by
Ieke Moerdijk
Introduction to foliations and Lie groupoids by
Ieke Moerdijk(
)
17 editions published between 2003 and 2008 in English and Italian and held by 1,606 WorldCat member libraries worldwide
Based on a graduate course taught at Utrecht University, this book provides a short introduction to the theory of Foliations and Lie Groupoids to students who have already taken a first course in differential geometry. Ieke Moerdijk and Janez Mrcun include detailed references to enable students to find the requisite background material in the research literature. The text features many exercises and worked examples
17 editions published between 2003 and 2008 in English and Italian and held by 1,606 WorldCat member libraries worldwide
Based on a graduate course taught at Utrecht University, this book provides a short introduction to the theory of Foliations and Lie Groupoids to students who have already taken a first course in differential geometry. Ieke Moerdijk and Janez Mrcun include detailed references to enable students to find the requisite background material in the research literature. The text features many exercises and worked examples
Algebraic set theory by
André Joyal(
)
14 editions published between 1995 and 2002 in English and Undetermined and held by 1,175 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
14 editions published between 1995 and 2002 in English and Undetermined and held by 1,175 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
Classifying spaces and classifying topoi by
Ieke Moerdijk(
Book
)
24 editions published between 1995 and 2008 in English and held by 535 WorldCat member libraries worldwide
This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory
24 editions published between 1995 and 2008 in English and held by 535 WorldCat member libraries worldwide
This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory
Sheaves in geometry and logic : a first introduction to topos theory by
Saunders MacLane(
Book
)
24 editions published between 1992 and 2005 in 3 languages and held by 486 WorldCat member libraries worldwide
An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic
24 editions published between 1992 and 2005 in 3 languages and held by 486 WorldCat member libraries worldwide
An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic
Simplicial methods for operads and algebraic geometry by
Ieke Moerdijk(
)
20 editions published between 2010 and 2011 in English and held by 484 WorldCat member libraries worldwide
"This book is an introduction to two highercategorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"Foreword
20 editions published between 2010 and 2011 in English and held by 484 WorldCat member libraries worldwide
"This book is an introduction to two highercategorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"Foreword
Models for smooth infinitesimal analysis by
Ieke Moerdijk(
Book
)
19 editions published between 1991 and 2011 in English and held by 327 WorldCat member libraries worldwide
The aim of this book is to construct categories of spaces which contain all the C?manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?manifolds will be explained
19 editions published between 1991 and 2011 in English and held by 327 WorldCat member libraries worldwide
The aim of this book is to construct categories of spaces which contain all the C?manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?manifolds will be explained
Proper maps of toposes by
Ieke Moerdijk(
Book
)
12 editions published in 2000 in English and held by 274 WorldCat member libraries worldwide
We develop the theory of compactness of maps between toposes, together with associated notions of separatedness. This theory is built around two versions of "propriety" for topos maps, introduced here in a parallel fashion. The first, giving what we simply call "proper" maps, is a relatively weak condition due to Johnstone. The second kind of proper maps, here called "tidy", satisfy a stronger condition due to Tierney and Lindgren. Various forms of the BeckChevalley condition for (lax) fibered product squares of toposes play a central role in the development of the theory. Applications include a version of the Reeb stability theorem for toposes, a characterization of hyperconnected Hausdorff toposes as classifying toposes of compact groups, and of strongly Hausdorff coherent toposes as classifiying toposes of profinite groupoids. Our results also enable us to develop further particular aspects of the factorization theory of geometric morphisms studied by Johnstone. Our final application is a (socalled lax) descent theorem for tidy maps between toposes. This theorem implies the lax descent theorem for coherent toposes, conjectured by Makkai and proved earlier by Zawadowski
12 editions published in 2000 in English and held by 274 WorldCat member libraries worldwide
We develop the theory of compactness of maps between toposes, together with associated notions of separatedness. This theory is built around two versions of "propriety" for topos maps, introduced here in a parallel fashion. The first, giving what we simply call "proper" maps, is a relatively weak condition due to Johnstone. The second kind of proper maps, here called "tidy", satisfy a stronger condition due to Tierney and Lindgren. Various forms of the BeckChevalley condition for (lax) fibered product squares of toposes play a central role in the development of the theory. Applications include a version of the Reeb stability theorem for toposes, a characterization of hyperconnected Hausdorff toposes as classifying toposes of compact groups, and of strongly Hausdorff coherent toposes as classifiying toposes of profinite groupoids. Our results also enable us to develop further particular aspects of the factorization theory of geometric morphisms studied by Johnstone. Our final application is a (socalled lax) descent theorem for tidy maps between toposes. This theorem implies the lax descent theorem for coherent toposes, conjectured by Makkai and proved earlier by Zawadowski
Sets, models and proofs by
Ieke Moerdijk(
)
5 editions published in 2018 in English and held by 132 WorldCat member libraries worldwide
This textbook provides a concise and selfcontained introduction to mathematical logic, with a focus on the fundamental topics in firstorder logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzenstyle natural deduction and a detailed proof of Gödel’s completeness theorem for firstorder logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for selfstudy, though it is ideally suited as a text for a onesemester university course in the second or third year.
5 editions published in 2018 in English and held by 132 WorldCat member libraries worldwide
This textbook provides a concise and selfcontained introduction to mathematical logic, with a focus on the fundamental topics in firstorder logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzenstyle natural deduction and a detailed proof of Gödel’s completeness theorem for firstorder logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for selfstudy, though it is ideally suited as a text for a onesemester university course in the second or third year.
Algebraic Set Theory(
)
2 editions published in 1995 in Undetermined and English and held by 35 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
2 editions published in 1995 in Undetermined and English and held by 35 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
Classical finite transformation semigroups : an introduction by
Olexandr Ganyushkin(
)
2 editions published in 2009 in Undetermined and English and held by 30 WorldCat member libraries worldwide
"The aim of this monograph is to give a selfcontained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, crosssections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers."Jacket
2 editions published in 2009 in Undetermined and English and held by 30 WorldCat member libraries worldwide
"The aim of this monograph is to give a selfcontained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, crosssections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers."Jacket
Sets, Models and Proofs by
Ieke Moerdijk(
)
1 edition published in 2018 in English and held by 22 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 22 WorldCat member libraries worldwide
Morphological features and conditions on rules in Montague grammar by
Fred Landman(
Book
)
1 edition published in 1981 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 1981 in English and held by 12 WorldCat member libraries worldwide
An alpine bouquet of algebraic topology : Alpine Algebraic and Applied Topology Conference, August 1521, 2016, SaasAlmagell,
Switzerland by Alpine algebraic and applied topology conference(
Book
)
3 editions published in 2018 in English and held by 9 WorldCat member libraries worldwide
This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in SaasAlmagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinitycategories and Segal spaces, equivariant homotopy theory, algebraic Ktheory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology
3 editions published in 2018 in English and held by 9 WorldCat member libraries worldwide
This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in SaasAlmagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinitycategories and Segal spaces, equivariant homotopy theory, algebraic Ktheory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology
Topics in intuitionism and topos theory by
Ieke Moerdijk(
)
3 editions published in 1985 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1985 in English and held by 9 WorldCat member libraries worldwide
Presentations of étendues by
Anders Kock(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Local equivalence relations and their sheaves by
Anders Kock(
Book
)
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Cohomology theories in synthetic differential geometry by
I Moerdijk(
Book
)
3 editions published in 1983 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1983 in English and held by 4 WorldCat member libraries worldwide
Spaces with local equivalence relations, and their monodromy by
Anders Kock(
Book
)
3 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
The tangent functor category revisited by
I Moerdijk(
Book
)
2 editions published in 1983 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1983 in English and held by 3 WorldCat member libraries worldwide
Connected locally connected toposes are pathconnected by
I Moerdijk(
Book
)
2 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
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Associated Subjects
Algebra Algebraic topology Cell aggregationMathematics Classifying spaces Combinatorial analysis Foliations (Mathematics) Geometry Geometry, Algebraic Global analysis (Mathematics) Grothendieck categories Group theory Homotopy theory Ktheory Lie groupoids Logic, Symbolic and mathematical Mappings (Mathematics) Mathematics Nonstandard mathematical analysis Operads Ordered algebraic structures Proof theory Semigroups Set theory Sheaf theory Simplexes (Mathematics) Toposes
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Alternative Names
Ieke Moerdijk Dutch mathematician
Ieke Moerdijk Hollandi matemaatik
Ieke Moerdijk matemàtic neerlandès
Ieke Moerdijk matematician olandez
Ieke Moerdijk matemático neerlandés
Ieke Moerdijk mathématicien néerlandais
Ieke Moerdijk Nederlands wiskundige, hoogleraar aan de Radboud Universiteit Nijmegen
Ieke Moerdijk niederländischer Mathematiker
Moerdijk, I.
Moerdijk, I. 1958
Moerdijk, I. (Ieke)
Moerdijk, I. (Ieke), 1958
Moerdijk, I. (Izak)
Moerdijk, Ieke
Moerdijk, Izak.
Moerdijk, Izak 1958
Moerdyk, Izak 1958
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