02017cam a2200241 i 4500 on1129467545 OCoLC ta 210520s2020 si a b 001 0 eng 9789811205101 (hardcover) 9811205108 (hardcover) (OCoLC)1129467545 (OCoLC)1100784131 QA169 .G736 2020 Grandis, Marco. Higher dimensional categories : from double to multiple categories / Marco Grandis. Singapore : World Scientific, c2020. xi, 522 p. : ill. Includes bibliographical references and index. A review of basic category theory -- Introducing two-dimensional category theory -- Double categories -- Double adjunctions -- Double limits -- Weak and lax multiple categories -- Multiple adjunctions -- Monads and algebras for multiple categories. "The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions. We want to show the advantages of this form for the theory of adjunctions and limits. Furthermore, this form is much simpler in higher dimension, starting with dimension three where weak 3-categories (also called tricategories) are already quite complicated, much more than weak or lax triple categories. This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories"-- Categories (Mathematics) lcc BK 0 0 0 0 PNLIB PNLIB GEN 2021-06-17 QA169 .G736 2020 PNLIB21062213 2021-06-17 2021-06-17 BK 2400 2400