Represents the state of the art in the new field of synthetic differential topology.

This book, first published in 2006, details how limit processes can be represented algebraically.

A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.

Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.

A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.

This book is a collection of best selected research papers presented at the International Conference on Communication and Artificial Intelligence (ICCAI 2021), held in the Department of Electronics & Communication Engineering, GLA University, Mathura, India, during 19–20 November 2021. The primary focus of the book is on the research information related to artificial intelligence, networks, and smart systems applied in the areas of industries, government sectors, and educational institutions worldwide. Diverse themes with a central idea of sustainable networking solutions are discussed in the book. The book presents innovative work by leading academics, researchers, and experts from industry.