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Category Theory

e-books in Category Theory category

Book cover: Notes on Category Theory with examples from basic mathematicsNotes on Category Theory with examples from basic mathematics
by - arXiv ,
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.
(739 views)
Book cover: Category Theory in ContextCategory Theory in Context
by - Dover Publications ,
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.
(6487 views)
Book cover: Categorical Homotopy TheoryCategorical Homotopy Theory
by - Cambridge University Press ,
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 ...
(4612 views)

Book cover: Seven Sketches in Compositionality: An Invitation to Applied Category TheorySeven Sketches in Compositionality: An Invitation to Applied Category Theory
by - arXiv.org ,
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.
(6577 views)
Book cover: Category Theory for ProgrammersCategory Theory for Programmers
by - unglue.it ,
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.
(7233 views)
Book cover: Category Theory for the SciencesCategory Theory for the Sciences
by - The MIT Press ,
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.
(7740 views)
Book cover: Basic Category TheoryBasic Category Theory
by - arXiv ,
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.
(8547 views)
Book cover: Dynamical Systems and SheavesDynamical Systems and Sheaves
by - arXiv ,
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.
(7072 views)
Book cover: Category Theory: A Gentle IntroductionCategory Theory: A Gentle Introduction
by - Logic Matters ,
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.
(7920 views)
Book cover: Combinatorics and Algebra of Tensor CalculusCombinatorics and Algebra of Tensor Calculus
by - arXiv ,
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.
(6526 views)
Book cover: Category Theory for ScientistsCategory Theory for Scientists
by - arXiv ,
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.
(10304 views)
Book cover: Categories and Homological AlgebraCategories and Homological Algebra
by - UPMC ,
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.
(10281 views)
Book cover: Category Theory for Computing ScienceCategory Theory for Computing Science
by - Prentice Hall ,
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.
(10145 views)
Book cover: Banach Modules and Functors on Categories of Banach SpacesBanach Modules and Functors on Categories of Banach Spaces
by - Marcel Dekker Inc ,
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.
(10761 views)
Book cover: Functors and Categories of Banach SpacesFunctors and Categories of Banach Spaces
by - Springer ,
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.
(10882 views)
Book cover: Category Theory and Functional ProgrammingCategory Theory and Functional Programming
by - University of St. Andrews ,
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.
(12906 views)
Book cover: Higher Topos TheoryHigher Topos Theory
by - Princeton University Press ,
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.
(13387 views)
Book cover: Higher AlgebraHigher Algebra
by - Harvard University ,
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.
(18440 views)
Book cover: Introduction to Categories and Categorical LogicIntroduction to Categories and Categorical Logic
by - arXiv ,
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.
(12848 views)
Book cover: Category Theory Lecture NotesCategory Theory Lecture Notes
by - University of Edinburgh ,
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.
(11973 views)
Book cover: Category Theory Lecture NotesCategory Theory Lecture Notes
by ,
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.
(12094 views)
Book cover: Category TheoryCategory Theory
- Wikibooks ,
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.
(12159 views)
Book cover: Basic Category TheoryBasic Category Theory
by - University of Utrecht ,
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.
(12899 views)
Book cover: Abelian Categories: an Introduction to the Theory of FunctorsAbelian Categories: an Introduction to the Theory of Functors
by - Harper and Row ,
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.
(13725 views)
Book cover: Model Categories and Simplicial MethodsModel Categories and Simplicial Methods
by - Northwestern University ,
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.
(10108 views)
Book cover: Notes on Categories and GroupoidsNotes on Categories and Groupoids
by - Van Nostrand Reinhold ,
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.
(15417 views)
Book cover: Seminar on Triples and Categorical Homology TheorySeminar on Triples and Categorical Homology Theory
by - Springer ,
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.
(11861 views)
Book cover: Higher Operads, Higher CategoriesHigher Operads, Higher Categories
by - arXiv ,
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.
(12750 views)
Book cover: Higher-Dimensional Categories: an illustrated guide bookHigher-Dimensional Categories: an illustrated guide book
by - University of Sheffield ,
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.
(13522 views)
Book cover: Mixed MotivesMixed Motives
by - American Mathematical Society ,
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.
(15036 views)
Book cover: A Gentle Introduction to Category Theory: the calculational approachA Gentle Introduction to Category Theory: the calculational approach
by - University of Twente ,
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.
(19450 views)
Book cover: Computational Category TheoryComputational Category Theory
by ,
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.
(19000 views)
Book cover: Categories, Types, and StructuresCategories, Types, and Structures
by - MIT Press ,
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.
(18903 views)
Book cover: Abstract and Concrete Categories: The Joy of CatsAbstract and Concrete Categories: The Joy of Cats
by - John Wiley & Sons ,
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.
(20093 views)
Book cover: Basic Concepts of Enriched Category TheoryBasic Concepts of Enriched Category Theory
by - Cambridge University Press ,
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.
(13599 views)
Book cover: Toposes, Triples and TheoriesToposes, Triples and Theories
by - Springer-Verlag ,
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.
(14919 views)