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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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