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Links to Free Computer, Mathematics, Technical Books all over the World



Computational Category Theory (David E. Rydeheard,, et al.)
This book is an implementation of concepts and constructions from category theory in the functional programming language Standard ML. It it proceeds from algorithm to algorithm until all of elementary category theory is laid out in precise computational form.

Category Theory: A Programming Language Oriented Introduction
This book explains the following topics: Categories, functors, natural transformations, String diagrams, Kan extensions, Algebras, coalgebras, bialgebras, Lambdacalculus and categories.

An Invitation to Applied Category Theory: Seven Sketches
Category theory is now a powerful tool in science, informatics, and industry. This book offers a selfcontained tour of applied category theory. Each chapter follows a single thread motivated by a realworld application and discussed with categorytheoretic tools.

Category Theory in Context (Emily Riehl)
This book introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.

Simplicial and Dendroidal Homotopy Theory (Gijs Heuts, et al)
This open access book offers a selfcontained introduction to the Homotopy Theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy.

Topology: A Categorical Approach (TaiDanae Bradley, et al)
A graduatelevel textbook that presents basic topology from the perspective of category theory. Many graduate students are familiar with the ideas of pointset topology and they are ready to learn something new about them.

Basic Category Theory (Tom Leinster)
Assuming little mathematical background, this short introduction to Category Theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time.

Category Theory for the Sciences (David I. Spivak)
Using databases as an entry to Category Theory, this book explains category theory by examples, and shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences.

Category Theory for Programmers (Bartosz Milewski)
In this category theory for programmers, the author illustrates all major concepts using computer code. You are probably aware that functional languages are closer to math than the more popular imperative languages. They also offer more abstracting power.

Category Theory for Computing Science (Michael Barr, et al.)
This book is a textbook in basic category theory, written specifically to be read by people in computing science. It expounds the constructions we feel are basic to category theory in the context of examples and applications to computing science.

Categories, Types, and Structures (Andrea Asperti, et al)
This book introduces Category Theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design. It pursues the more complex mathematical semantics of data types and programs.

Categorical Homotopy Theory (Emily Riehl)
This book develops abstract Homotopy Theory from the categorical perspective with a particular focus on examples. It helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

Sheaf Theory through Examples (Daniel Rosiak)
Taking an applied category theory perspective, this book provides an approachable introduction to elementary sheaf theory and examines applications. It seeks to bridge the powerful results of sheaf theory as used by mathematicians and realworld applications,

Higher Topos Theory (Jacob Lurie)
This book presents the foundations of Higher Topos 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.

Programming in MartinLof's Type Theory: An Introduction
This book focuses on the type theory developed by Per MartinLof. It contains a thorough introduction to the MartinLof's Type Theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

Proofs and Types (JeanYves Girard, et al.)
Deals with the mathematical background of the application to computer science of aspects of logic on typed lambda calculus (namely the correspondence between propositions and types). Treats both the traditional logic and its applications to computer science.

Type Theory and Functional Programming (Simon Thompson)
This book explores the role of MartinLof's constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice.
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