Basic Category Theory
arxiv.org
Basic Category Theory
1–10 of 92 posts
Re: Basic Category Theory
#2"for readers with relatively little mathematical background."
A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative identities. ;-)
Re: Basic Category Theory
#3"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree?
Additionally, what are applications of category theory to computer programming, or computer science in general? I find this really interesting from an outsiders view and want to learn it. I'm looking for a truly basic and gentle approach to learning category theory, without removing the rigor.
Re: Basic Category Theory
#4"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
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Re: Basic Category Theory
#5"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree? Additionally, what are applications of category theory to comp…
You might be interested in "Algebra: Chapter 0" http://amzn.to/2iYpAn5
"The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics."
Re: Basic Category Theory
#6"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
The "note to the reader" clarifies things a bit -- he's aiming for requiring "no more mathematical knowledge than might be acquired from an undergraduate degree at an ordinary British university". Though he does not specify whether he has in mind a mathematics degree, I think this can be deduced from the fact that he indicates that the text developed out of a master's-level course.
Re: Basic Category Theory
#7"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree? Additionally, what are applications of category theory to comp…
The mathematical background assumed here is the content of the first couple weeks of the first upper-level course in an undergraduate mathematics degree. It really is "relatively little mathematical background".
That said, I second the recommendation of "Algebra: Chapter 0".
Re: Basic Category Theory
#8Earlier quoted context omitted.
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree? Additionally, what are applications of category theory to comp…
You might be interested in "Algebra: Chapter 0" http://amzn.to/2iYpAn5 "The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics."
Thanks, but is this another textbook that requires knowledge in abstract algebra prior to reading it, or make any sort of previous knowledge assumptions?
Re: Basic Category Theory
#9"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree? Additionally, what are applications of category theory to comp…
It feels like "relatively little" to many authors means "a complete set of undergrad math courses from a fairly math-heavy major" (which could be something like calculus including vectors, differential equations, linear algebra, real analysis, and maybe abstract algebra and discrete math). Maybe we need another term for "OK with logic, proofs, and calculations and doesn't mind learning notation, but hasn't had a lot of university-level courses, or in any event doesn't remember them".
Re: Basic Category Theory
#10"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
Why do mathematicians use phrases such as "relatively little mathematical background" or "introduction to.." when they assume previous knowledge? I find that really annoying and a turn off from reading most math textbooks that are suppose to be "introductions". Is there an actual good book on category theory for someone that didn't complete a math degree? Additionally, what are applications of category theory to comp…
I think it's easily done when someone knows a topic too well to teach it to beginners from outside the field. Rings, fields and identities may just be math's equivalents of string, operator, or variable, when similarly used by introductory programming books without any explanation.