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Sheaves in geometry and logic: a first introduction to topos theory

- Saunders MacLane Galdós, I. Moerdijk
- Mathematics
- 1992

This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various… Expand

Introduction to Foliations and Lie Groupoids

- I. Moerdijk, J. Mrčun
- Mathematics
- 13 October 2003

This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an… Expand

Axiomatic homotopy theory for operads

- C. Berger, I. Moerdijk
- Mathematics
- 10 June 2002

Abstract
We give sufficient conditions for the existence of a model
structure on operads in an arbitrary symmetric monoidal model
category. General invariance properties for homotopy algebras
over… Expand

Models for smooth infinitesimal analysis

- I. Moerdijk, G. Reyes
- Mathematics
- 17 December 1990

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… Expand

Algebraic set theory

- A. Joyal, I. Moerdijk
- Mathematics
- 1995

1. Axiomatic theory of small maps 2. Zermelo-Fraenkel algebras 3. Existence theorems 4. Examples.

Orbifolds, sheaves and groupoids

- I. Moerdijk, D. Pronk
- Mathematics
- 1 July 1997

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds… Expand

Deformations of Lie brackets: cohomological aspects

- M. Crainic, I. Moerdijk
- Mathematics, Physics
- 25 March 2004

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid.

Wellfounded trees in categories

- I. Moerdijk, E. Palmgren
- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 15 July 2000

TLDR

Monads on tensor categories

- I. Moerdijk
- Mathematics
- 23 March 2002

Abstract A Hopf monad is a monad on a tensor category, equipped with comparison maps relating the monad structure to the tensor structure. We study some general properties of such Hopf monads, their… Expand

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