## 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

## 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

## 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

## 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

## : 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

## 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

## Frege's Account of Classes

*Michael Potter*

### in Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

In the Grundlagen, Frege sketched a proof of the basic properties of natural numbers from the numerical equivalence and showed how that equivalence could be proved if numbers were explicitly defined ... 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