01604 a2200193 4500003002100000005001700021008004100038020001800079040002500097082002000122100002700142245008900169260004100258300002900299504005000328505055300378520045400931650002501385ISI Library, Kolkata20200929120628.0200929b ||||| |||| 00| 0 eng d a9789811205101 aISI LibrarybEnglish04223a512.6bG753 aGrandis, Marcoeauthor aHigher Dimensional Categories: bfrom double to multiple categories /cMacro Grandis bWorld Scientific,c2019aNew Jersey: axi, 522 pages,c23.5 cm. aIncludes bibliographical references and index aIntroduction --
Part I From Categories to Double Categories -- A Review of Basic Category Theory -- Introducing Two-Dimensional Category Theory -- Double Categories -- Double Adjunctions -- Double Limits --
Part II Multiple Categories -- Weak and Lax Multiple Categories -- Multiple Adjunctions -- Monads and Algebras for Multiple Categories --
Appendix A -- Applications in Homological Algebra and Algebraic Topology --
Appendix B -- Symmetric Cubical Sets and Cubical Categories --
Appendix C -- Solutions and Hints --
References --
Index aThis 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. 4aAlgebraic Categories