This book presents a new semiotic theory based upon category theory and applying to a classification of creativity in music and mathematics. It is the first functorial approach to mathematical semiotics that can be applied to AI implementations for c...Lasīt vairāk
Sērija : Memoirs of the American Mathematical Society
(Izdošanas datums: 09-May-2019, PDF+DRM, Izdevniecība: American Mathematical Society, ISBN-13: 9781470453213)
In 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type D_4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn moti...Lasīt vairāk
(Izdošanas datums: 02-Mar-2016, PDF+DRM, Izdevniecība: Princeton University Press, ISBN-13: 9781400881796)
Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ? an abelian group K0? or K1? respectively. Professor Milnor sets out, in the present work, to define and study an anal...Lasīt vairāk
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoin...Lasīt vairāk
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint...Lasīt vairāk
(Izdošanas datums: 09-Jul-2011, PDF+DRM, Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, ISBN-13: 9783642217746)
This work introduces tools, from the field of category theory, that make it possible to tackle until now unsolvable representation problems (determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it a...Lasīt vairāk
(Izdošanas datums: 10-Mar-2010, PDF+DRM, Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, ISBN-13: 9783642112973)
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories an...Lasīt vairāk
Sērija : Memoirs of the American Mathematical Society
(Izdošanas datums: 01-Sep-2017, PDF+DRM, Izdevniecība: American Mathematical Society, ISBN-13: 9781470441357)
The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory \operatorname{OpdBim}_{\mathcal{V}} of operad bimodules, that has operads as 0-cells, operad bimodules as 1-cells and operad b...Lasīt vairāk
Sērija : Memoirs of the American Mathematical Society
(Izdošanas datums: 01-May-2000, PDF+DRM, Izdevniecība: American Mathematical Society, ISBN-13: 9781470402747)
First I will introduce a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can...Lasīt vairāk
Christian Ausoni, Kathryn Hess, Brenda Johnson, Wolfgang Luck, Jerome Scherer
Sērija : Contemporary Mathematics
(Izdošanas datums: 01-Jun-2014, PDF+DRM, Izdevniecība: American Mathematical Society, ISBN-13: 9781470416850)
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, func...Lasīt vairāk
