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# Category Theory

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## e-books in this category

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**Category Theory for the Sciences**

by **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.

(**367** views)

**Basic Category Theory**

by **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.

(**939** views)

**Dynamical Systems and Sheaves**

by **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.

(**825** views)

**Category Theory: A Gentle Introduction**

by **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.

(**1155** views)

**Categories and Modules**

by **Takahiro Kato** - **viXra.org** , **2015**

Modules and morphisms among them subsume categories and functors and provide more general framework to explore the theory of structures. In this book we generalize the basic notions and results of category theory using this framework of modules.

(**2177** views)

**Combinatorics and Algebra of Tensor Calculus**

by **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.

(**2167** views)

**Category Theory for Scientists**

by **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.

(**4123** views)

**Categories and Homological Algebra**

by **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.

(**4068** views)

**Category Theory for Computing Science**

by **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.

(**4224** views)

**Banach Modules and Functors on Categories of Banach Spaces**

by **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.

(**4775** views)

**Functors and Categories of Banach Spaces**

by **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.

(**4776** views)

**Category Theory and Functional Programming**

by **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.

(**6217** views)

**Higher Topos Theory**

by **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.

(**5803** views)

**Higher Algebra**

by **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.

(**8761** views)

**Introduction to Categories and Categorical Logic**

by **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.

(**5807** views)

**Category Theory Lecture Notes**

by **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.

(**5475** views)

**An Introduction to Category Theory in Four Easy Movements**

by **A. Schalk, H. Simmons** - **Manchester University** , **2005**

Notes for a course offered as part of the MSc. in Mathematical Logic. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.

(**6316** views)

**Category Theory Lecture Notes**

by **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.

(**5499** 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.

(**6009** views)

**Basic Category Theory**

by **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.

(**5987** views)

**Abelian Categories: an Introduction to the Theory of Functors**

by **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.

(**5764** views)

**Model Categories and Simplicial Methods**

by **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.

(**4561** views)

**Notes on Categories and Groupoids**

by **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.

(**9245** views)

**Seminar on Triples and Categorical Homology Theory**

by **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.

(**6121** views)

**Higher Operads, Higher Categories**

by **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.

(**6500** views)

**Higher-Dimensional Categories: an illustrated guide book**

by **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.

(**7171** views)

**Mixed Motives**

by **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.

(**8696** views)

**A Gentle Introduction to Category Theory: the calculational approach**

by **Maarten M. Fokkinga** , **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.

(**11913** views)

**Computational Category Theory**

by **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.

(**12592** views)

**Categories, Types, and Structures**

by **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.

(**10707** views)

**Abstract and Concrete Categories: The Joy of Cats**

by **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.

(**9643** views)

**Basic Concepts of Enriched Category Theory**

by **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.

(**7552** views)

**Toposes, Triples and Theories**

by **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.

(**8449** views)

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