e-books in Category Theory category
Notes on Category Theory with examples from basic mathematicsby Paolo Perrone - arXiv , 2021
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced mathematics.
(1454 views)
Category Theory in Contextby Emily Riehl - Dover Publications , 2016
This is a concise, original text for a one-semester introduction to the subject. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, monads, etc.
(7238 views)
Categorical Homotopy Theoryby Emily Riehl - Cambridge University Press , 2014
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Emily Riehl discusses two competing perspectives by which one typically first encounters homotopy (co)limits ...
(5136 views)
Seven Sketches in Compositionality: An Invitation to Applied Category Theoryby Brendan Fong, David I Spivak - arXiv.org , 2018
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.
(7205 views)
Category Theory for Programmersby Bartosz Milewski - unglue.it , 2017
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming.
(8014 views)
Category Theory for the Sciencesby David I. Spivak - The MIT Press , 2014
This book shows that category theory can be useful outside of mathematics as a flexible modeling language throughout the sciences. Written in an engaging and straightforward style, the book is rigorous but accessible to non-mathematicians.
(8389 views)
Basic Category Theoryby Tom Leinster - arXiv , 2016
This introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. For each new concept a generous supply of examples is provided.
(9263 views)
Dynamical Systems and Sheavesby D. I. Spivak, C. Vasilakopoulou, P. Schultz - arXiv , 2016
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time.
(7637 views)
Category Theory: A Gentle Introductionby Peter Smith - Logic Matters , 2016
I hope that what is here may prove useful to others starting to get to grips with category theory. This text is intended to be relatively accessible; in particular, it presupposes rather less mathematical background than some texts on categories.
(8740 views)
Combinatorics and Algebra of Tensor Calculusby Sen Hu, Xuexing Lu, Yu Ye - arXiv , 2015
In this paper, we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
(7080 views)
Category Theory for Scientistsby David I. Spivak - arXiv , 2013
We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based.
(10868 views)
Categories and Homological Algebraby Pierre Schapira - UPMC , 2011
These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
(10831 views)
Category Theory for Computing Scienceby Michael Barr, Charles Wells - Prentice Hall , 1998
This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions basic to category theory in the context of applications to computing science.
(10839 views)
Banach Modules and Functors on Categories of Banach Spacesby J. Cigler, V. Losert, P.W. Michor - Marcel Dekker Inc , 1979
This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.
(11324 views)
Functors and Categories of Banach Spacesby Peter W. Michor - Springer , 1978
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
(11553 views)
Category Theory and Functional Programmingby Mikael Vejdemo-Johansson - University of St. Andrews , 2012
An introduction to category theory that ties into Haskell and functional programming as a source of applications. Topics: definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases, etc.
(13475 views)
Higher Topos Theoryby Jacob Lurie - Princeton University Press , 2009
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
(14138 views)
Higher Algebraby Jacob Lurie - Harvard University , 2017
Contents: Stable infinite-Categories; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules; Little Cubes and Factorizable Sheaves; Algebraic Structures on infinite-Categories; and more.
(19765 views)
Introduction to Categories and Categorical Logicby Samson Abramsky, Nikos Tzevelekos - arXiv , 2011
These notes provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
(13388 views)
Category Theory Lecture Notesby Daniele Turi - University of Edinburgh , 2001
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.
(12509 views)
Category Theory Lecture Notesby Michael Barr, Charles Wells , 1999
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
(12910 views)
Category Theory- Wikibooks , 2010
This book is an introduction to category theory, written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. It contains examples drawn from various branches of math.
(12863 views)
Basic Category Theoryby Jaap van Oosten - University of Utrecht , 2007
Contents: Categories and Functors; Natural transformations; (Co)cones and (Co)limits; A little piece of categorical logic; Adjunctions; Monads and Algebras; Cartesian closed categories and the lambda-calculus; Recursive Domain Equations.
(13535 views)
Abelian Categories: an Introduction to the Theory of Functorsby Peter Freyd - Harper and Row , 1964
From the table of contents: Fundamentals (Contravariant functors and dual categories); Fundamentals of Abelian categories; Special functors and subcategories; Metatheorems; Functor categories; Injective envelopes; Embedding theorems.
(14293 views)
Model Categories and Simplicial Methodsby Paul Goerss, Kristen Schemmerhorn - Northwestern University , 2004
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.
(10670 views)
Notes on Categories and Groupoidsby P. J. Higgins - Van Nostrand Reinhold , 1971
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(16211 views)
Seminar on Triples and Categorical Homology Theoryby B. Eckmann - Springer , 1969
This volume concentrates a) on the concept of 'triple' or standard construction with special reference to the associated 'algebras', and b) on homology theories in general categories, based upon triples and simplicial methods.
(12493 views)
Higher Operads, Higher Categoriesby Tom Leinster - arXiv , 2003
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from topology, quantum algebra, mathematical physics, logic, and computer science.
(13382 views)
Higher-Dimensional Categories: an illustrated guide bookby Eugenia Cheng, Aaron Lauda - University of Sheffield , 2004
This work gives an explanatory introduction to various definitions of higher-dimensional category. The emphasis is on ideas rather than formalities; the aim is to shed light on the formalities by emphasizing the intuitions that lead there.
(14236 views)
Mixed Motivesby Marc Levine - American Mathematical Society , 1998
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry.
(15777 views)
A Gentle Introduction to Category Theory: the calculational approachby Maarten M. Fokkinga - University of Twente , 1994
These notes present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. This text introduces category theory in the calculational style of the proofs.
(20047 views)
Computational Category Theoryby D.E. Rydeheard, R.M. Burstall , 2001
The book is a bridge-building exercise between computer programming and category theory. Basic constructions of category theory are expressed as computer programs. It is a first attempt at connecting the abstract mathematics with concrete programs.
(19745 views)
Categories, Types, and Structuresby Andrea Asperti, Giuseppe Longo - MIT Press , 1991
Here is an introduction to category theory for the working computer scientist. It is a self-contained introduction to general category theory and the mathematical structures that constitute the theoretical background.
(19592 views)
Abstract and Concrete Categories: The Joy of Catsby Jiri Adamek, Horst Herrlich, George Strecker - John Wiley & Sons , 1990
A modern introduction to the theory of structures via the language of category theory, the emphasis is on concrete categories. The first five chapters present the basic theory, while the last two contain more recent research results.
(20956 views)
Basic Concepts of Enriched Category Theoryby Max Kelly - Cambridge University Press , 2005
The book presents a selfcontained account of basic category theory, assuming as prior knowledge only the most elementary categorical concepts. It is designed to supply a connected account of the theory, or at least of a substantial part of it.
(14177 views)
Toposes, Triples and Theoriesby Michael Barr, Charles Wells - Springer-Verlag , 2005
Introduction to toposes, triples and theories and the connections between them. The book starts with an introduction to category theory, then introduces each of the three topics of the title. Exercises provide examples or develop the theory further.
(15499 views)