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 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: Categories, functors, natural
transformations, String diagrams, Kan extensions, Algebras, coalgebras,
bialgebras, Lambda-calculus and categories.
Purpose 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 taken-for-granted ideas, either by exposing
existing weaknesses or flaws in our understanding, or by highlighting hidden
commonalities across scientific fields.
This note covers the following topics related to Category Theory: Notation, Basic Definitions, Sum and Product, Adjunctions, Cartesian Closed
Categories, Algebras and Monads.
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 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 2-Categories.
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.