I was a software researcher of a certain Japanese company. I retired the company in April 2014 when I was 55 yeas old.
Recently I realized Category Theory is important for software/computer science and started to study it by reading text books.
I think there are some kinds of hurdles to understand the category theory for the person without enough maturity of mathematics. To tell the truth, category theory is too difficult (for me).
This is a picture of person in the sea of abstract algebra.
This picture is the reuse of
semigroup theory's picture. Please put appropriate words in the category theory at the waves.
Studying the category theory by oneself requires a lot of patience and causes fears such as
While it is important to study the theory steadily, proving the theorems carefully,
it is also useful
In this site, I write
For the time being, I will make
Lastly, please note the following might contain my misunderstandings, since I am also studying them.
Logic Matters : Category TheoryDr. Peter Smith is a person who wrote the following simple introduction of Galois connection used to understand the relationship between logical systems and its interpretation structures. This paper is very easy to understand.
The Galois Connection between Syntax and SemanticsI wrote a very simple introduction of the paper. Please refer to here
He (Peter Smith) also wrote a text book for category theory.
Peter Smith: : Category Theory: A Gentle Introduction, 2016The adjective "Gentle Introduction" sounds sweet.
This is a famous text book. It contains topics in computer science, lambda-calculus, logic, etc.
I wrote
a short explanation of the whole contents. Please press the picture or here.
This book does not contain computer science topics. It is a very thin book that enables relatively rapid study. It contains full of examples and seems to try to tell vivid images to readers.
I wrote
a short explanation of the whole contents. Please press the picture or here.
The autor is Dr. Peter Smith I wrote just above.
The title says this book is
In the beginning of chapter 4, the author says that this book is slow space for the readers without enough maturity of mathematics. Chapter 1 to 12 (page i - page 119) are about the topics inside categories. chapter 13 to chapter 27 are about the topics between categories. The polycy and structure of the book are contrast to Leinster's "Basic Category Theory". Leinster's book introduces "Adjoints" very fast.
At the day of 9th Oct. 2017, the chapters after "25 Adjoints introduce" are not yet stable, they may be changed.
This book is trying to tell background knowledge of concepts that are described only technically in other (usual) text books. For example, it has three chapters concerning natural transformations, "18 Natural isomorphism", "19 Natural transformations and functor categories", "20 Equivalent categories" roughly corresponding to the "chapter 7 Naturality" of Awodey's "Category Theory". I used those chapters as complemented information (mainly about "background rationale of the concepts introduced) when I read Awodey's chapter 7.
The phrase
Though this book is published from MIT Press, the PDF of its previous version is available freely at
David I. Spivak, "Category Theory for Scientists (Old Version)", September 17, 2013"
I bound the printed material by my self( binding method (written in Japanese)) and began to read.
(the rest is to be filled)
It is very short lecture note of 75 pages in total, 37 pages about basics of category theory. Therefore, it can be used to grasp the whole figure of category theory very rapidly.
Moreover, this lecture note contains case studies, the examples of applications of category theory to computer sciences. Case studies have 4 sections,
Since this lecture note is a little old, readers should look for recent research results after having grasped the whole figure of category theory and applications to computer science by this lecture note.
This is published by Dover Publications. Thus, the price would be reasonable to many learners. The PDF seems to be available at the author's web site. Seeing the her web site, she seems to be active to music, sports, wide range of talents except the category theory.
While I have not yet read it, since I found many its good reputations I printed the PDF and added to the list to be read.
Topics in this book seems to be inside mathematics and does not contain computer science^{1)} basically. My criteria to mathematics books seems to be
The contents of this book are
1) This book contains the phrase "computer science" about 10 times, "currying" that is "A x B -> C is isomorphic to A -> B -> C", "Maybe monad", etc.(the rest is to be filled)
Just to make sure, I write the definition of monad simply. A monad is defined to be a triple of an endofunctor T : C -> C and two natural transformations η : id -> T and μ : T^{2} -> T that satisfies some conditions similar to the conditions of monoid.
I have alread written this above. There are listed up full of resources of category theory. Moreover, we can get knowledges about Logic.
Very interesting site explaining the category theory relating to the functional programming language Haskel. In his site, sometimes, pretty pigs appear kindly to explain us easily and funny. He (not a pig, Bartosz Milewski) also put his videos about category theory to youtube. The videos are also very interesting and funny sometimes.
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