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View Code? Open in Web Editor NEWA book about category theory
Home Page: https://abuseofnotation.github.io/category-theory-illustrated/
A book about category theory
Home Page: https://abuseofnotation.github.io/category-theory-illustrated/
Search for "the the", it appears twice on the text.
Another: "For example here is a function which that takes an argument"
Also, "than that function" should be "then that function"
I tried to open a pull request but I didn't have permission to open a branch.
Excellent book! It's already in a very mature stage.
In the picture of is letter function https://github.com/abuseofnotation/category-theory-illustrated/blob/master/_chapters/01_set/char_boolean.svg two mappings are incorrect:
'z' - points to false
'#' - points to true
Technically it is still correct function (by definition of function), but it returns incorrect results, which might be confusing.
Hello!
First of all, I'd like to thank all the contributors for their contributions to this project.
I find it useful and I believe, such resources like this should be available in different formats as well.
I have seen that it is also possible to have a PDF format of the website, but ePub
format is better than this as
it has better compatibility with book applications and you may have more tools (for note taking, highlighting, section and whatnot) compared to PDF, even though most of these are also available for PDF.
So this issue I open is about the possibility of whether the epub
could also be provided maybe in releases section of this repository or on the website.
Thank you in advance.
Hi,
Thanks for your great work.
Could you tell me what is the software you used for creating this beautiful figure https://boris-marinov.github.io/category-theory-illustrated/cover.svg ?
Thanks in advance.
This is a great book. I really wish I had it back at the university where all was explained with symbols only.
Here is a few typos / broken links I found:
For example, squaring a number is a function from the set of real numbers to the set of real positive numbers
That should read: to the set of real non-negative numbers.
The example even shows 0 being mapped to 0.
The arrows in this diagram are pointing in the wrong direction.
In the "Singleton Set" section it says:
The set of books written by the American writer Harper Lee and published during her lifetime is a singleton set - she has published just one novel.
Which isn't quite true, since 2015 she published "Go Set a Watchman".
I know this is being pedantic and not the point of the explanation, but I guess it could confuse someone who knows a lot more about American literature than set theory.
I find your explanations and graphics excellent and I am wondering if there is an open source or CreativeCommons-type of license attached to it that would allow fair sharing of parts of the content.
#7 was closed with no libre license officially added, and the permission given was extremely vague and ambiguous.
So as to avoid any legal trouble, please may you make the licensing official and add a libre license?
On the orders
page, poset
is used without being defined, starting in the Greatest and Least
section.
Normally, I would just create a pull request to either define it at first use, or to replace all instances of poset with partial orders
or partially ordered sets
but it seems to me that the correct solution is one that respects the style and approach you are using throughout. E.g., using partially ordered sets instead of partial orders might require some explanation about being a little loose with the poset concept, since the text is concerned more with partial orders than posets, strictly speaking.
Great read, by the way, thank you very much for pulling this together.
When I open it directly at https://boris-marinov.github.io/category-theory-illustrated/02_category/isomorphism.svg, I get the following error:
This page contains the following errors:
error on line 3 at column 33: xmlns:i: '&ns_ai;' is not a valid URI
Below is a rendering of the page up to the first error.
Looking at the contents:
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
xmlns:i="&#38;#38;ns_ai;"
it probably should be xmlns:i="&#38;ns_ai;"
One antecedent needs to be q
In Monoids etc, we have:
When a rule is associative [...] we can add or remove a term that is present at both sides of an equation and retaining the equality of the existing terms:
An image follows that suggests that for elements x
, y
, z
and w
, if x y z = w z
then x y = w
. This is false; there's nothing that says w
has a right inverse. As a counterexample, take a commutative ring with a zero divisor, like k[X] / (X^3)
where k
is a field, and consider x = X
, y = X
, z = X
and w = X^2
. Then x y z = 0
and w z = 0
but x y = X^2
and w = X
.
Please review cases where it's should be it's. Example:
,,,
alter it’s state.
,,,
If I an not wrong an isomorphism is "structure-preserving bijection" i.e. "bijective homomorphism".
First chapter describes isomorphisms in context of plain sets that don't have structure. This is technically correct, but it may be more appropriate to use term "bijection" instead.
(I'm sorry if this is explained later in the book)
The symbols ∧ (AND), ∨(OR) and ¬(NOT) are very abstract. Using them in a diagram makes that diagram harder to understand intuitively. You sort of have to already know them to understand what is going on. Also more complicated diagrams require a lot of mental effort to parse, which is in stark contrast to the other chapters, where diagrams are elegant and intuitive.
I would like to suggest other symbols:
Have a red? curly? zigzaging? ring around the elements. This would work great for composition and would be easy to read even in more complicated diagrams (like when illustrating the rules of de morgan).
Have a rounded rectangle around the terms, signaling that they are connected and are now one term. A bit similar to a cartouche in egytian hieroglyphs
Have a rounded rectangle around the terms, but with a line separating the two terms.
To illustrate how easy these symbols would make visual parsing I have drawn a diagram of the de morgan rule:
x OR y = (NOT x) AND (NOT y)
(drawn in paint, I am ashamed by myself)
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