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Category Theory

Steve Awodey

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.001.0001
Subject:
Mathematics, Algebra

This book is a text and reference book on Category Theory, a branch of abstract algebra. The book contains clear definitions of the essential concepts, which are illuminated with numerous accessible ... More


Developing Cross Cultural Measurement

Thanh V. Tran

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195325089
eISBN:
9780199864515
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195325089.001.0001
Subject:
Social Work, Research and Evaluation

This book provides an overview of issues and techniques relevant to the development of cross-cultural measures and provides a step-by-step approach to the assessment of cross-cultural equivalence of ... More


An Introduction to Auction Theory

Flavio M. Menezes and Paulo K. Monteiro

Published in print:
2004
Published Online:
April 2005
ISBN:
9780199275984
eISBN:
9780191602214
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019927598X.001.0001
Subject:
Economics and Finance, Microeconomics

This book presents an in-depth discussion of the auction theory. It introduces the concept of Bayesian Nash equilibrium and the idea of studying auctions as games. Private, common, and affiliated ... More


Flips and Flops

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter presents a series of results that elucidate the relation between D-equivalence and K-equivalence. Derived categories are first studied. These results can then be used to show that the ... More


Triangulated Categories

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0001
Subject:
Mathematics, Geometry / Topology

Reviewing the basic notions of additive and abelian categories, left and right adjoint functors, and Serre functors, this chapter is mainly devoted to triangulated categories. In particular, criteria ... More


Derived Category and Canonical Bundle --II

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0006
Subject:
Mathematics, Geometry / Topology

Based on the work of Orlov, Kawamata, and others, this chapter shows that the (numerical) Kodaira dimension and the canonical ring are preserved under derived equivalence. The same techniques can be ... More


Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.001.0001
Subject:
Mathematics, Geometry / Topology

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a ... More


The View from General Relativity

Harvey R. Brown

in Physical Relativity: Space-time structure from a dynamical perspective

Published in print:
2005
Published Online:
September 2006
ISBN:
9780199275830
eISBN:
9780191603914
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199275831.003.0009
Subject:
Philosophy, Philosophy of Science

In his 1923 book The Mathematical Theory of Relativity, Arthur Eddington distinguished between two chains of reasoning in general relativity. The first familiar one starts with the existence of the ... More


Assessing Measurement Equivalence Assessing Measurement Equivalence

Thanh V. Tran

in Developing Cross Cultural Measurement

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195325089
eISBN:
9780199864515
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195325089.003.0006
Subject:
Social Work, Research and Evaluation

In comparative research — whether it is cross-cultural, cross-national, or multigroup comparison — the assumption of measurement equivalence is crucially important. If nonequivalent measures were ... More


Testing Cross-Cultural Measurement Invariance: LISREL Applications LISREL Applications

Thanh V. Tran

in Developing Cross Cultural Measurement

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195325089
eISBN:
9780199864515
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195325089.003.0007
Subject:
Social Work, Research and Evaluation

There has been a general consensus that multigroup (sample) confirmatory factor analysis offers a strong approach to evaluate cross-cultural equivalence of measurement properties. Researchers have ... More


Conclusion of the Proof

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0017
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the tools to prove that the proof of Theorem 1.2 is reduced to Statement G. It begins with the lemma stating that the cardinality of each Γ‎-pack or Δ‎-pack is a power of 2. It ... More


Over-Arching Issues

Anthony B. Atkinson

in New Sources of Development Finance

Published in print:
2004
Published Online:
January 2005
ISBN:
9780199278558
eISBN:
9780191601590
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199278555.003.0002
Subject:
Economics and Finance, Development, Growth, and Environmental

This chapter, together with chs. 10 to 11, approaches the question of development funding in a theoretical way, rather than by examining individual proposals for sources. Chapter 2 itself deals with ... More


Translation Technique

Philip Burton

in The Old Latin Gospels: A Study of their Texts and Language

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198269885
eISBN:
9780191600449
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198269889.003.0005
Subject:
Religion, Early Christian Studies

An analysis of the conceptual framework for analysing the translation technique of the Old Latin Gospels. The terminology found in Cicero, Augustine, and Jerome is summarized, along with modern terms ... More


THE PARTIAL ORDER OF GRAPHS AND HOMOMORPHISMS

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0003
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the order homomorphisms induce on the set of all cores; this order is rich enough to represent all countable partial orders. Antichains in the homomorphism order are discussed, ... More


 Going, Going …

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0021
Subject:
Economics and Finance, Microeconomics

The most successful area of game theory is auction design. This chapter offers a short review of the subject. Various traditional auctions are described. After showing that most of these generate the ... More


FUNCTORS AND NATURALITY

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0007
Subject:
Mathematics, Algebra

This chapter develops a general theory for functors. Topics discussed include category of categories, representable structure, stone duality, naturality, examples of natural transformations, ... More


: The Singleness of the Categorical Imperative

Henry E. Allison

in Essays on Kant

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199647033
eISBN:
9780191741166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199647033.003.0010
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

This essay defends Kant's thesis that there is only a single categorical imperative. This needs a defense because in the Groundwork Kant presents a number of formulations of this imperative (the ... More


Linear Quadratic Approximations: An Introduction

Javier Díaz‐Giménez

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0002
Subject:
Economics and Finance, Macro- and Monetary Economics

This is a brief introduction to dynamic programming and the method of using linear quadratic (LQ) approximations to the return function; the method is an approximation because it computes the ... More


CARDINAL COLLAPSING, BOOLEAN ISOMORPHISM, AND APPLICATIONS TO THE THEORY OF BOOLEAN ALGEBRAS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses the following topics: the collapsing of a cardinal to a smaller one in a Boolean-valued model; infinitary equivalence of structures as Boolean isomorphism; and the use of ... More


Processing Stages and Strategies

R. Duncan Luce

in Response Times: Their Role in Inferring Elementary Mental Organization

Published in print:
1991
Published Online:
January 2008
ISBN:
9780195070019
eISBN:
9780199869879
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195070019.003.0012
Subject:
Psychology, Cognitive Models and Architectures

This chapter discusses the ability of serial and parallel models to mimic either an arbitrary response-time distribution or just one another. The results vary both in what is assumed to be observable ... More


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