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Author: Gregory Maxwell Kelly
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 254
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Book Description
Author: Gregory Maxwell Kelly
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 254
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Book Description
Author: Nick Gurski
Publisher: Cambridge University Press
ISBN: 1107034892
Category : Mathematics
Languages : en
Pages : 287
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Book Description
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
ISBN: 1475747217
Category : Mathematics
Languages : en
Pages : 320
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Book Description
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author: John C. Baez
Publisher: Springer Science & Business Media
ISBN: 1441915362
Category : Algebra
Languages : en
Pages : 292
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Book Description
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Author: Robert Gordon
Publisher: American Mathematical Soc.
ISBN: 0821803441
Category : Mathematics
Languages : en
Pages : 94
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Book Description
This work defines the concept of tricategory as the natural 3-dimensional generalization of bicategory. Trihomomorphism and triequivalence for tricategories are also defined so as to extend the concepts of homomorphism and biequivalence for bicategories.
Author: Michael Fullan
Publisher: Corwin Press
ISBN: 150630172X
Category : Education
Languages : en
Pages : 114
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Book Description
Complex times call for clear solutions—If initiative overload and fragmentation are keeping your best plans from becoming reality, it’s time to start leading differently. The key to bringing about the kind of successful and sustainable change you need is the Coherence Framework, a dynamic, customizable road map made up of four essential components: Focused direction to build collective purpose Cultivating collaborative cultures while clarifying individual and team roles Deepening learning to accelerate improvement and foster innovation Securing accountability from the inside out Coherence provides the insights and tools to drive effective leadership. Now you can gain a deeper understanding of Coherence with The Taking Action Guide to Building Coherence in Schools, Districts, and Systems. Coherence is a book that demands action – it moves from the narrative of fixing one teacher at a time, to asking about the coherence of the system (be it school, national, or world issues). Fullan and Quinn create an important narrative about direction, working together, deepening learning, and securing accountability. The book sparkles with examples of coherence in action, it makes no excuses for employing the wrong levers of change. This is the blueprint for a new vocabulary of education action; it shows where we need to go next, and is another example of Fullan at the top of his game. John Hattie Director, Melbourne Education Research Institute and Author of Visible Learning "School systems that struggle are riddled with incoherence—mismatched strategies, competing cultures, and illogical initiatives. Fullan and Quinn explain clearly how coherence can solve the problem. Based on solid research and lessons drawn from effective practice, Coherence provides a comprehensive model to guide educators as they learn and lead their way to better schools." Susan Moore Johnson Jerome T. Murphy Research Professor Harvard Graduate School of Education
Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 0521532159
Category : Mathematics
Languages : en
Pages : 451
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Book Description
Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Author: Niles Johnson
Publisher: Oxford University Press, USA
ISBN: 0198871376
Category : Mathematics
Languages : en
Pages : 636
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Book Description
2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Author: Alan Watkins
Publisher: Kogan Page Publishers
ISBN: 0749470062
Category : Business & Economics
Languages : en
Pages : 352
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Book Description
Every business leader faces innumerable challenges every working day, each one taking their toll on precious energy levels and the ability to respond and react positively in a commercial environment. Coherence recognizes the key factors that take their toll on a leader's effectiveness and ability to lead, and provides the reader with unique solutions designed to improve physiological factors that impact on core competencies. Problems today cannot be solved with yesterday's level of thinking. CEOs fail and leaders burn out because our thinking has not sped up or powered up. The author not only recognizes that leaders have the potential for limitless processing power, but shows them how to access it, taking them back to fundamentals and, quite literally, to the heart of who we are and how we function successfully. By showing leaders how to be 'younger, smarter, healthier and happier' Coherence gives every decision maker the power to make influential decisions under pressure and achieve sustainable success at every level.
Author: Noson S. Yanofsky
Publisher: MIT Press
ISBN: 026238079X
Category : Computers
Languages : en
Pages : 669
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Book Description
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
