*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 ...
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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 examples. It provides full proofs of all the important propositions and theorems, and aims to make the basic ideas, theorems, and methods of Category Theory understandable. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; and monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided.Less

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 examples. It provides full proofs of all the important propositions and theorems, and aims to make the basic ideas, theorems, and methods of Category Theory understandable. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; and monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided.

*Steve Awodey*

- 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, ...
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This chapter develops a general theory for functors. Topics discussed include category of categories, representable structure, stone duality, naturality, examples of natural transformations, exponentials of categories, functor categories, and equivalence of categories. The chapter ends with some exercises.Less

This chapter develops a general theory for functors. Topics discussed include category of categories, representable structure, stone duality, naturality, examples of natural transformations, exponentials of categories, functor categories, and equivalence of categories. The chapter ends with some exercises.

*Annalisa Primi*

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780231175180
- eISBN:
- 9780231540773
- Item type:
- chapter

- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231175180.003.0006
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter seeks to answer the question of what lessons Africa can learn from the experiences in Latin America given the changing global landscapes that both regions face in pursuing economic ...
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This chapter seeks to answer the question of what lessons Africa can learn from the experiences in Latin America given the changing global landscapes that both regions face in pursuing economic transformation today with the “new geography” of growth, production, trade, and innovation as a result of the rise of emerging economies, especially China.Less

This chapter seeks to answer the question of what lessons Africa can learn from the experiences in Latin America given the changing global landscapes that both regions face in pursuing economic transformation today with the “new geography” of growth, production, trade, and innovation as a result of the rise of emerging economies, especially China.

*Steven Phillips and William H. Wilson*

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262027236
- eISBN:
- 9780262322461
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027236.003.0009
- Subject:
- Philosophy, Philosophy of Mind

A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary ...
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A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary (ad hoc) modifications to close explanatory gaps. Cognitive capacities are systematically distributed around common structures. Category theory, a mathematical theory of structure, provides a framework for a theory of systematicity that explains the nature of these structures. Underlying each collection of systematically related capacities is a categorical universal construction: each capacity is uniquely composed of a common (universal) component and capacity-specific component; constructions not admitting this form of compositionality are not categorical universal constructions. Hence, our category theoretical explanation transcends problems with other (classical/symbolic, connectionist) approaches, which admit both systematic and non-systematic architectures.Less

A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary (ad hoc) modifications to close explanatory gaps. Cognitive capacities are systematically distributed around common structures. Category theory, a mathematical theory of structure, provides a framework for a theory of systematicity that explains the nature of these structures. Underlying each collection of systematically related capacities is a categorical universal construction: each capacity is uniquely composed of a common (universal) component and capacity-specific component; constructions not admitting this form of compositionality are not categorical universal constructions. Hence, our category theoretical explanation transcends problems with other (classical/symbolic, connectionist) approaches, which admit both systematic and non-systematic architectures.