Moerdijk, Ieke
Overview
Works:  96 works in 232 publications in 4 languages and 4,751 library holdings 

Roles:  Author, Thesis advisor 
Classifications:  QA3, 512.55 
Publication Timeline
.
Most widely held works by
Ieke Moerdijk
Sheaves in geometry and logic : a first introduction to topos theory by
Saunders Mac Lane(
Book
)
19 editions published between 1992 and 2005 in 3 languages and held by 410 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
19 editions published between 1992 and 2005 in 3 languages and held by 410 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
Algebraic set theory by
André Joyal(
Book
)
17 editions published between 1995 and 2002 in English and Undetermined and held by 339 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
17 editions published between 1995 and 2002 in English and Undetermined and held by 339 WorldCat member libraries worldwide
This book offers a new, algebraic, approach to set theory
Classifying spaces and classifying topoi by
Ieke Moerdijk(
Book
)
22 editions published between 1992 and 2008 in English and held by 330 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
22 editions published between 1992 and 2008 in English and held by 330 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
Models for smooth infinitesimal analysis by
Ieke Moerdijk(
Book
)
16 editions published between 1991 and 2010 in English and held by 258 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
16 editions published between 1991 and 2010 in English and held by 258 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
Introduction to foliations and Lie groupoids by
Ieke Moerdijk(
Book
)
15 editions published between 2003 and 2008 in English and Italian and held by 238 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
15 editions published between 2003 and 2008 in English and Italian and held by 238 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
Proper maps of toposes by
Ieke Moerdijk(
Book
)
11 editions published in 2000 in English and held by 237 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
11 editions published in 2000 in English and held by 237 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
Simplicial methods for operads and algebraic geometry by
Ieke Moerdijk(
Book
)
21 editions published between 2010 and 2011 in English and held by 70 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
21 editions published between 2010 and 2011 in English and held by 70 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
Morphological features and conditions on rules in Montague grammar by
Fred Landman(
Book
)
2 editions published in 1981 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 14 WorldCat member libraries worldwide
Topics in intuitionism and topos theory by
Ieke Moerdijk(
)
2 editions published in 1985 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 1985 in English and held by 9 WorldCat member libraries worldwide
Local equivalence relations and their sheaves by
Anders Kock(
Book
)
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
A definiability theorem for first order logic by
C Butz(
Book
)
4 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Classifying Spaces and Classifying Topoi by
Ieke Moerdijk(
)
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
The classifying topos of a continuous groupoid by
Ieke Moerdijk(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Presentations of étendues by
Anders Kock(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
Cohomology theories in synthetic differential geometry by
Ieke 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
Ruimte voor de logica by
Ieke Moerdijk(
Book
)
1 edition published in 1997 in Dutch and held by 3 WorldCat member libraries worldwide
1 edition published in 1997 in Dutch and held by 3 WorldCat member libraries worldwide
Local maps of Grothendieck toposes by
Ieke Moerdijk(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Continuous fibrations and inverse limits of toposes by
Ieke 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
Category theory and its applications : dedicated to professor Bill Lawvere(
Book
)
1 edition published in 2000 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 3 WorldCat member libraries worldwide
Classical finite transformation semigroups : an introduction by
Olexandr Ganyushkin(
)
1 edition published in 2009 in English and held by 0 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
1 edition published in 2009 in English and held by 0 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
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Kids  General  Special 
Related Identities
 Mrc̆un, J. 1966 Other Author
 Joyal, André Author
 Toën, Bertrand 1973
 Mac Lane, Saunders 19092005 Author
 Reyes, Gonzalo E. 1937
 Vermeulen, J. J. C. (Jacob Johan Caspar) 1957
 Kock, Joachim 1967
 Casacuberta, Carles 1961 Editor
 Joyal, Andri Author
 Joyal, André (1943....) Author
Useful Links
Associated Subjects
Algebra Algebraic topology Categories (Mathematics) Cell aggregationMathematics Classifying spaces Combinatorial analysis Foliations (Mathematics) 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 Semigroups Set theory Sheaf theory Simplexes (Mathematics) Toposes
Alternative Names
Ieke Moerdijk Dutch mathematician
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
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