Elements of 8-Category Theory

von Emily Riehl, Dominic Verity

770 Seiten, Hardcover

Kurzbeschreibung des Verlags

The language of ¿-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ¿-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ¿-categories from first principles in a model-independent fashion using the axiomatic framework of an ¿-cosmos, the universe in which ¿-categories live as objects. An ¿-cosmos is a fertile setting for the formal category theory of ¿-categories, and in this way the foundational proofs in ¿-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

• Reihe: Cambridge Studies in Advanced Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Topologie
• ISBN: 9781108837989
• Sprache: Englisch
• Erscheinungsdatum: 10.02.2022
• Größe: 232 x 159 mm
• Verlag: Cambridge University Press