Towards A Definition Of Topos
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Towards A Definition of Topos
Allegories, rhetoric, imagery, commonplaces, cliches and archetypes are discussed in connection with the literary work of authors such as Montaigne, Shakespeare, Jules Verne, Emile Zola and James Joyce.
Aristotle's Topics
This work deals with Aristotle's Topics, a textbook on how to argue successfully in a debate organised in a certain way. The origins of the three branches of logic can be found here: logic of propositions, of predicates and of relations. Having dealt with the structure of the dialectical debates and the theory of the predicables, the central notion of the topos is analysed. Topoi are principles of arguments designed to help a disputant refute his opponent and function as hypotheses in hypothetical syllogisms, the main form of argument in the Topics. Traces of the crystallization of their theory can be found in the Topics and Analytics. The author analyses a selection of topoi including those according to which categorical and relational syllogisms are constructed.
Towards Higher Categories
Author: John C. Baez
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-09-24
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.