Mac Lane, Categories For The Working Mathematician Pdf
- Saunders Maclane Categories For The Working Mathematician Pdf
- Mac Lane Categories For The Working Mathematician Pdf Compressor
- Categories For The Working Mathematician Pdf
Author: Saunders MacLane Editor: Springer Science & Business Media ISBN: Size: 10,22 MB Format: PDF, ePub, Docs Read: 401 Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe maticians working in a variety of other fields of Mathematical research.
The book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. It is very well-written, with plenty of interesting discussions and stimulating exercises.” (Ittay Weiss, MAA Reviews, July, 2014) Second Edition S.M. Lane Categories for the Working Mathematician 'A very useful introduction to category theory.'
Product Description Categories for the Working Mathematician provides 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. The book 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 characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. Mac Lane attempted to settle an ambiguity in usage for the terms epimorphism and monomorphism by introducing the terms epic and monic, but the distinction is not in common use.
Categories with Finite Products 72 6. Groups in Categories 75 7. Colimits of Representable Functors 76 IV. Adjoints 79 1. Adjunctions 79 2. Top free app for mac 2014. Examples of Adjoints 86 3. Reflective Subcategories 90 4. Equivalence of Categories 92 5. Adjoints for Preorders 95 6. Cartesian Closed Categories 97 7. Transformations of Adjoints 99 8. Composition of Adjoints 103 9.
Categories for the Working MathematicianPreface to the Second EditionPreface to the First EditionContentsIntroductionI. Categories, Functors, and Natural TransformationsII. Constructions on CategoriesIII. Universals and LimitsIV. Monads and AlgebrasVII. Abelian CategoriesIX. Special LimitsX.
Saunders Maclane Categories For The Working Mathematician Pdf
Categories for the Working MathematicianSaunders Mac Lane 1 / 5Publisher: SpringerRelease Date: 2 / 5ISBN: Author: Saunders Mac LaneDownload Here3 / 5array of general ideas useful in a wide variety of fields. Starting from the foundations, this bookilluminates the concepts of category, functor, natural transformation, and duality. It then turns toadjoint functors, which provide a description of universal constructions, an analysis of therepresentations of functors by sets of morphisms, and a means of manipulating direct and inverselimits. These categorical concepts are extensively illustrated in the remaining chapters, which includemany applications of the basic existence theorem for adjoint functors. The categories of algebraicsystems are constructed from certain adjoint-like data and characterised by Beck's theorem.
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Mac Lane Categories For The Working Mathematician Pdf Compressor
I highly recommend 'Categories for the Working Mathematician' not only to my fellow working mathematicians but also to anyone with an interest in higher mathematics as there are almost no prerequisites for this self-contained masterpiece.
Categories For The Working Mathematician Pdf
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