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The language of 8-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic …
This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model …
Practical Foundations collects the methods of construction of the objects of twentieth century mathematics. Although it is mainly concerned with a framework essentially equivalent …
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an …
This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal …
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an …
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which …
Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound …
The theory of natural dualities, as presented in this text, is broad enough to encompass many known dualities through a rich assortment of substantive theorems, yet concrete enough …