Conceptual Mathematics A First Introduction To Categories By Lawvere And Schanuel
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Conceptual Mathematics
Author: F. William Lawvere
language: en
Publisher: Cambridge University Press
Release Date: 1997-10-09
In the last fifty years, the use of the notion of 'category' has led to a remarkable unification and simplification of mathematics. Written by two of the best known participants in this development, Conceptual Mathematics is the first book to serve as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists etc. While the ideas and techniques of basic category theory are useful throughout modern mathematics, this book does not presuppose knowledge of specific fields but rather develops elementary categories such as directed graphs and discrete dynamical systems from the beginning. The fundamental ideas are then illuminated in an engaging way by examples in these categories.
Conceptual Mathematics and Literature
The old practices of interpretation have been exhausted, and the humanities and social sciences are facing a crisis. Is there a way out of the labyrinth of reading? In this book, Professor Neuman presents a challenging approach to interpreting texts and reading literature through the spectacles of conceptual mathematics. This approach strives to avoid the simplicity of a quantitative approach to the analysis of literature as well as both the relativistic and the ideological dangers facing a qualitative reading of a text. The approach is introduced in a rigorous and accessible manner and woven with insights gained from various fields. Taking us on a challenging journey from Ovid’s Metamorphoses to Nick Cave’s The Death of Bunny Munro, the book shows how we may gain a deeper understanding of literature and the aesthetic experience of reading.
Category Theory And Applications: A Textbook For Beginners (Second Edition)
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.