From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10005 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: A book on Higher Dimensional Categories Date: Wed, 18 Sep 2019 17:29:07 +0200 Message-ID: Reply-To: Marco Grandis Mime-Version: 1.0 (Apple Message framework v1085) Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="262885"; mail-complaints-to="usenet@blaine.gmane.org" To: Original-X-From: majordomo@rr.mta.ca Thu Sep 19 01:04:58 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1iAj0L-0016DS-T1 for gsmc-categories@m.gmane.org; Thu, 19 Sep 2019 01:04:58 +0200 Original-Received: from rr.mta.ca ([198.164.44.159]:50054) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1iAiyu-0008Oy-2p; Wed, 18 Sep 2019 20:03:28 -0300 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1iAipP-00064F-08 for categories-list@rr.mta.ca; Wed, 18 Sep 2019 19:53:39 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:10005 Archived-At: This book is being published: M. Grandis Higher Dimensional Categories, =46rom Double to Multiple Categories World Scientific Publishing Co., 2019 - Info at WS:=20 https://www.worldscientific.com/worldscibooks/10.1142/11406 - Downloadable Introduction https://www.worldscientific.com/doi/pdf/10.1142/9789811205118_0001 ________ PREFACE 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 self-study and research. Notions are = presented in a concrete way, with examples and exercises; the latter are = endowed with a solution or suitable hints. Part I, devoted to double = categories, starts at basic category theory and is kept at a relatively = simple level. Part II can be used independently by a reader with some = knowledge of 2-dimensional category theory. ________ The following exposition of my talk at CT2019, in Edinburgh, can also be = viewed as a partial introduction to this book: "Adjunctions and limits for double and multiple categories" http://www.dima.unige.it/~grandis/CT%202019%20Edi.pdf ________ Regards, MG= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]