WorldCat Identities

Moerdijk, Ieke

Overview
Works: 99 works in 268 publications in 3 languages and 4,971 library holdings
Roles: Author, Other, Thesis advisor, 956, Opponent
Publication Timeline
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Most widely held works by Ieke Moerdijk
Sheaves in geometry and logic : a first introduction to topos theory by Saunders Mac Lane( Book )

23 editions published between 1992 and 2005 in 3 languages and held by 422 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 )

20 editions published between 1995 and 2010 in English and Undetermined and held by 345 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 Undetermined and held by 329 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 )

17 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 242 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 )

12 editions published in 2000 in English and held by 236 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 Beck-Chevalley 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 (so-called 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 )

20 editions published between 2010 and 2011 in English and held by 72 WorldCat member libraries worldwide

"This book is an introduction to two higher-categorical 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

Topics in intuitionism and topos theory by Ieke Moerdijk( )

3 editions published in 1985 in English and held by 10 WorldCat member libraries worldwide

A definiability theorem for first order logic by Carsten Butz( Book )

4 editions published in 1997 in English and held by 4 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

Cohomology theories in synthetic differential geometry by Ieke Moerdijk( Book )

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

Continuous fibrations and inverse limits of toposes by Ieke Moerdijk( Book )

3 editions published in 1984 in English and held by 4 WorldCat member libraries worldwide

Presentations of étendues by Anders Kock( Book )

3 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide

Local maps of Grothendieck toposes by Ieke Moerdijk( Book )

3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide

The classifying topos of a continuous groupoid by Ieke Moerdijk( Book )

3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide

Smooth spaces versus continuous spaces in models for synthetic differential geometry by Ieke Moerdijk( Book )

3 editions published in 1983 in English and held by 3 WorldCat member libraries worldwide

The tangent functor category revisited by Ieke Moerdijk( Book )

2 editions published in 1983 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 self-contained 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, cross-sections 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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Audience level: 0.50 (from 0.03 for Introducti ... to 0.95 for A definiab ...)

Sheaves in geometry and logic : a first introduction to topos theory
Alternative Names
Ieke Moerdijk Dutch mathematician

Ieke Moerdijk matemàtic neerlandès

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-

Languages
English (160)

Italian (2)

German (1)

Covers
Algebraic set theoryClassifying spaces and classifying topoiModels for smooth infinitesimal analysisIntroduction to foliations and Lie groupoidsProper maps of toposesSimplicial methods for operads and algebraic geometry