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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

## Derived Categories: A Quick Tour

*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/9780199296866.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter briefly outlines the main steps in the construction of the derived category of an arbitrary abelian category. The homotopy category of complexes is considered as an intermediate step, ... More

## The Skeleton

*Hagit Borer*

### in Structuring Sense: Volume III: Taking Form

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199263936
- eISBN:
- 9780191759017
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263936.003.0006
- Subject:
- Linguistics, Theoretical Linguistics, Syntax and Morphology

This chapter returns to the general model, and offers a perspective on phrase structure, constituent structure, linearization and functors. While Chomsky's Bare Phrase Structure is adopted, the ... More

## Conclusion

*Hagit Borer*

### in Structuring Sense: Volume III: Taking Form

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199263936
- eISBN:
- 9780191759017
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263936.003.0013
- Subject:
- Linguistics, Theoretical Linguistics, Syntax and Morphology

This chapter provides a summary of the major results presented in the book, as well as an overview of their significance, particularly in light of past and future research agendas. A summary is ... More

## Diagrams of Structure: Categories and Functors

*Rocco Gangle*

### in Diagrammatic Immanence: Category Theory and Philosophy

- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9781474404174
- eISBN:
- 9781474418645
- Item type:
- chapter

- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9781474404174.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter introduces the elementary concepts and operations of category theory. It introduces the notion of category by generalizing from partial orders and systems of functions and then ... More

## Diagrams of Difference: Adjunctions and Topoi

*Rocco Gangle*

### in Diagrammatic Immanence: Category Theory and Philosophy

- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9781474404174
- eISBN:
- 9781474418645
- Item type:
- chapter

- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9781474404174.003.0007
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter examines two advanced constructions in category theory: adjoint functors and topoi. Pairs of adjoint functors, or adjunctions, are formally defined and then illustrated with several ... More

## Representability of Moduli Problems

*Kai-Wen Lan*

### in Arithmetic Compactifications of PEL-Type Shimura Varieties

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691156545
- eISBN:
- 9781400846016
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691156545.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter elaborates on the representability of the moduli problems defined in the previous chapter. The treatment here is biased towards the prorepresentability of local moduli and Artin's ... More

## Introduction—Words? What Words?

*Hagit Borer*

### in Structuring Sense: Volume III: Taking Form

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199263936
- eISBN:
- 9780191759017
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263936.003.0001
- Subject:
- Linguistics, Theoretical Linguistics, Syntax and Morphology

This chapter provides an introduction to the book as a whole. It begins with a detailed critical review of historical approaches to Words, focusing, in particular, on the rationale for listedness and ... More

## Categorizing Roots

*Hagit Borer*

### in Structuring Sense: Volume III: Taking Form

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199263936
- eISBN:
- 9780191759017
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263936.003.0007
- Subject:
- Linguistics, Theoretical Linguistics, Syntax and Morphology

This chapter is devoted to articulating a model of categorial determination based fundamentally on the conceptualization of categorial selection as a partition of the categorial space, and as ... More

## The category of roots

*Hagit Borer*

### in The Syntax of Roots and the Roots of Syntax

- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780199665266
- eISBN:
- 9780191748554
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199665266.003.0006
- Subject:
- Linguistics, Syntax and Morphology, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

This chapter focuses on the categorial properties of roots and proposes that, just like event structure, these emerge in the context of particular functional structure and as a consequence of it. For ... More

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