This 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 Andruskiewitsch-Schneider conjecture, The Cartier-Kostant
theorem, Pivotal categories and dimensions, Spherical categories and
Grothendieck rings of semisimple tensor categories.
Author(s): P.
Etingof, S. Gelaki, D. Nikshych, and V. Ostrik
This note covers the following topics: Preliminaries, Categories, Properties of objects
and arrows, Functors, Diagrams and naturality, Products and sums, Cartesian
closed categories, Limits and colimits, Adjoints, Triples, Toposes and
Categories with monoidal structure.
Author(s): Department of Mathematics
and Statistics,McGill University
This PDF book covers the
following topics related to Category Theory : All concepts are Kan extensions,
Derived functors via deformations, Basic concepts of enriched category theory,
The unreasonably effective bar construction, Homotopy limits and colimits:
the practice, Weighted limits and colimits, Categorical tools for homotopy limit
computations, Weighted homotopy limits and colimits, Derived enrichment, Weak
factorization systems in model categories, Algebraic perspectives on the small
object argument, Enriched factorizations and enriched lifting properties, A
brief tour of Reedy category theory,. Preliminaries on quasi-categories,
Simplicial categories and homotopy coherence, Isomorphisms in quasi-categories,
A sampling of 2-categorical aspects of quasi-category theory.
This
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.
This 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.
This 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, 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.
This 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 Andruskiewitsch-Schneider conjecture, The Cartier-Kostant
theorem, Pivotal categories and dimensions, Spherical categories and
Grothendieck rings of semisimple tensor categories.
Author(s): P.
Etingof, S. Gelaki, D. Nikshych, and V. Ostrik
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,
2-Categories and Fibered Categories.
This 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.
This 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 Curry-Howard-Lambek Isomorphism, Induction and
Coinduction, Stream programming examples and Monads.
This 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.
Author(s): Graham
Hutton, School of Computer Science, University of Nottingham
This 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.