000			02017cam a2200241 i 4500
001			on1129467545
003			OCoLC
007			ta
008			210520s2020 si a b 001 0 eng
020			_a9789811205101 _q(hardcover)
020			_a9811205108 _q(hardcover)
035			_a(OCoLC)1129467545 _z(OCoLC)1100784131
050			_aQA169 _b.G736 2020
100	1		_aGrandis, Marco.
245	1	0	_aHigher dimensional categories : _bfrom double to multiple categories / _cMarco Grandis.
260			_aSingapore : _bWorld Scientific, _cc2020.
300			_axi, 522 p. : _bill.
504			_aIncludes bibliographical references and index.
505	0		_aA 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.
520			_a"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"--
650		4	_aCategories (Mathematics)
942			_2lcc _cBK
999			_c2400 _d2400