

This section contains free ebooks and guides on Category Theory, some of the resources in this section can be viewed online and some of them can be downloaded.




An introduction to Category TheoryHarold
SimmonsPDF  436 Pages  EnglishThe book is aimed primarily at the beginning graduate
student.It gives the de nition of this notion, goes through the various
associated gadgetry such as functors, natural transformations, limits and
colimits, and then explains adjunctions.
 Introduction To Category Theory And Categorical LogicThomas StreicherPDF  117 Pages  EnglishThis
note covers the following topics related to Category Theory: Categories,
Functors and Natural Transformations, subcategories, Full and Faithful Functors,
Equivalences, Comma Categories and Slice Categories, Yoneda Lemma, Grothendieck
universes, Limits and Colimits, Adjoint Functors, Adjoint Functor Theorems,
Monads, Elementary Toposes, Cartesian Closed Categories, Logic of Toposes and
Sheaves.
  Category Theory by Prof. Dr. B. PareigisProf. Dr. B. PareigisPDF  90 Pages  EnglishThis book
explains the following topics related to Category Theory:Foundations, Graphs,
Monoids, Categories, Constructions on categories, Functors, Special types of
functors, Natural transformations, Representable functors and the Yoneda Lemma,
Terminal and initial objects, The extension principle, Isomorphisms,
Monomorphisms and epimorphisms, Products, Adjoint functors and monads.
 Computational Category TheoryD.E. Rydeheard and R.M. BurstalPDF  263 Pages  EnglishThis book emphasizes
category theory in conceptual aspects, so that category theory has come to be
viewed as a theory whose purpose is to provide a certain kind of conceptual
clarity.
 Category Theory for ScientistsDavid I. SpivakOnline  NA Pages  EnglishPurpose of this course note
is to prove that category theory is a powerful language for understanding and
formalizing common scientific models. The power of the language will be tested
by its ability to penetrate into takenforgranted ideas, either by exposing
existing weaknesses or flaws in our understanding, or by highlighting hidden
commonalities across scientific fields.
 Lecture NotesCategory TheorySteve AwodeyOnline  NA Pages  EnglishCategory theory, a branch of abstract
algebra, has found many applications in mathematics, logic, and computer
science. Like such fields as elementary logic and set theory, category theory
provides a basic conceptual apparatus and a collection of formal methods useful
for addressing certain kinds of commonly occurring formal and informal problems,
particularly those involving structural and functional considerations. This
course note is intended to acquaint students with these methods, and also
to encourage them to reflect on the interrelations between category theory and
the other basic formal disciplines.
 Tensor Categorie (PDF 93P)P.
Etingof, S. Gelaki, D. Nikshych, and V. OstrikPDF  393 Pages  EnglishThis note covers the following
topics: Monoidal categories, The pentagon axiom, Basic properties of unit
objects in monoidal categories, monoidal categories, Monoidal functors,
equivalence of monoidal categories, Morphisms of monoidal functors, MacLane's
strictness theorem, The MacLane coherence theorem, Invertible objects,
Exactness of the tensor product, Semisimplicity of the unit object, Groupoids,
Finite abelian categories and exact faithful functors, Fiber functors, Hopf
algebras, Pointed tensor categories and pointed Hopf algebras, Chevalley's
theorem, The AndruskiewitschSchneider conjecture, The CartierKostant
theorem, Pivotal categories and dimensions, Spherical categories and
Grothendieck rings of semisimple tensor categories.
  Notes on Category Theory (PDF 416P)Robert L. KnightenPDF  416 Pages  English These notes are targeted to a student
with significant mathematical sophistication and a modest amount of specific
knowledge. Covered topics are: Mathematics in Categories, Constructing
Categories, Functors and Natural Transformations, Universal Mapping
Properties, Algebraic Categories, Cartesian Closed Categories, Monoidal
Categories, Enriched Category Theory, Additive and Abelian Categories,
2Categories and Fibered Categories.
 Category Theory Lecture Notes for ESSLLI (PDF 133P)Michael
Barr and Charles WellsPDF  133 Pages  EnglishThis note covers the following topics related to
Category Theory: Functional programming languages as categories, Mathematical structures as
categories, Categories of sets with structure, Categories of algebraic
structures, Constructions on categories, Properties of objects and arrows,
Functors, Diagrams and naturality, Products and sums, Cartesian closed
categories, Limits and colimits, Adjoints, Triples, Toposes, Categories with
monoidal structure.
 Brief notes on category theory (PDF 36P)Prakash PanangadenPDF  36 Pages  EnglishThis note
explains the following topics related to Category Theory: Duality, Universal and
couniversal properties, Limits and colimits, Biproducts in Vect and Rel,
Functors, Natural transformations, Yoneda'a Lemma, Adjoint Functors, Cartesian
Closed Categories, The CurryHowardLambek Isomorphism, Induction and
Coinduction, Stream programming examples and Monads.
 Introduction to The Theory of Categories  Higher Dimensional Categories an illustrated guide bookEugenia Cheng and Aaron
LaudaOnline  182 Pages  EnglishThis 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 emphasising the intuitions that
lead there. Covered topics are: Penon, Batanin and Leinster, Opetopic,
Tamsamani and Simpson, Trimble and May.
 Higher Operads, Higher CategoriesTom LeinsterOnline  NA Pages  EnglishHigher
dimensional category theory is the study of n categories, operads, braided
monoidal categories, and other such exotic structures. It draws its
inspiration from areas as diverse as topology, quantum algebra, mathematical
physics, logic, and theoretical computer science. This is the first book on
the subject and lays its foundations.
 Mixed Motives  Category Theory Lecture Notes (PDF 61P)Daniele
TuriPDF  61 Pages  EnglishThis note covers the following topics: Universal Problems, Basic Notions, Universality, Natural
Transformations and Functor Categories, Colimits, Duality and LKan
Extensions imits, Adjunctions, Preservation of Limits and Colimits, Monads,
Lawvere Theories, Cartesian Closed Categories, Variable Sets and Yoneda
Lemma and 2Categories.
 Introduction to Category TheoryGraham
Hutton, School of Computer Science, University of NottinghamOnline  NA Pages  EnglishThis note
teaches the basics of category theory, in a way that is accessible and
relevant to computer scientists. The emphasis is on gaining a good
understanding the basic definitions, examples, and techniques, so that
students are equipped for further study on their own of more advanced topics
if required.
 Category Theory Steve Awodey (PDF 314P)  Basic Category Theory (PDF 88p)Jaap van OostenPDF  88 Pages  EnglishThis note covers the following topics: Categories and Functors, Natural transformations,
Examples of natural transformations, Equivalence of categories, cones and
limits, Limits by products and equalizers, Colimits, A little piece of
categorical logic, The logic of regular categories.









