diff --git a/img/a-book-of-abstract-algebra.jpg b/img/a-book-of-abstract-algebra.jpg new file mode 100644 index 0000000..cf6f4d7 Binary files /dev/null and b/img/a-book-of-abstract-algebra.jpg differ diff --git a/img/abstract-algebra-cover.png b/img/abstract-algebra-cover.png new file mode 100644 index 0000000..b1d825d Binary files /dev/null and b/img/abstract-algebra-cover.png differ diff --git a/img/visual-group-theory.jpg b/img/visual-group-theory.jpg new file mode 100644 index 0000000..0196a38 Binary files /dev/null and b/img/visual-group-theory.jpg differ diff --git a/readme.org b/readme.org index a4956cc..08f6b4b 100644 --- a/readme.org +++ b/readme.org @@ -114,21 +114,37 @@ To make this case, let me first mention this book by Saunders Mac Lane, the co-i Now an adjacent field to Category Theory is Abstract Algebra. The route I have taken is to first learn abstract algebra which undergirds the algebraic species that are often subjects of study in Category Theory. To make sense of these, let me mention a few books. It is not mandatory reading, if you want to dive first into Category Theory. In fact some of the books that I have put together here allows one to learn Category Theory without much prerequisite knowledge but abstract algebra is a field that I have felt is most proximate and has aided me ease into Category Theory texts. -1/ A Book of Abstract Algebra by Charles Pinter + +#+BEGIN_HTML + +#+END_HTML + +** [[https://amzn.to/2S3SOVc][A Book of Abstract Algebra]] +*Charles Pinter* This book by Charles Pinter reads not like a textbook but like a description of the field. -2/ A Concrete Approach to Abstract Algebra by W. W. Sawyer +#+BEGIN_HTML + +#+END_HTML + +** [[https://archive.org/details/AConcreteApproachToAbstractAlgebra][A Concrete Approach to Abstract Algebra]] +*W. W. Sawyer* A narrative approach for Abstract Algebra is given by Sawyer by focussing on concrete applications. -3/ Visual Group Theory by Nathan Carter +#+BEGIN_HTML + +#+END_HTML + +** Visual Group Theory +*Nathan Carter* Visual Group Theory by Nathan Carter gives an overview of the field by relying on visualizations. His playground for the cayley diagram explorations gives a good idea of the quality of work that has gone into producing this book. I will try to expand on this catalogue once I have better perspective, but these three seem to be the most promising to get a good overview of the algebraic structures. -Once this is done, I’ll recommend starting with Category Theory texts. These works helps an enthusiast to get through the field to understand it deeper. +Once the above works are studied, starting with Category Theory texts should be an easy process. I will now proceed to list the works which will help an enthusiast to navigate the field of Category Theory and understand it deeper. * Visual Nature of Category Theory @@ -138,12 +154,21 @@ Once this is done, I’ll recommend starting with Category Theory texts. These w Category Theory is the study of objects and morphisms and for this purpose, I find it most important to have a visual setting for exploring these ideas. Many of the ideas being talked about in Category Theory spawns dynamic pictures of morphisms in my head, but I find it hard to visualize them as there is so little Category Theory with pictures around. What is pictured here is an animation by James McKeown of a modular lattice rotating on its vertical axis. These sort of algebraic structures are a part of what we study with Category Theory. And I think there is a certain truth to the idea that geometry is the missing link to ground the abstract ideas that is being studied under Category Theory. -I came across this talk by Jamie Vicary on building tools for exploring Category Theory. His works [[https://globular.science][Globular.science]] and [[https://homotopy.io][Homotopy.io]] are (awe)inspiring. Do check out his talk titled **Category Theory: Visual Mathematics for the 21st Century** and his works to see how he connects proofs, programs, and geometry together in a triad! +* Jamie Vicary’s work +I came across this talk by Jamie Vicary on building tools for exploring Category Theory. His works [[https://globular.science][Globular.science]] and [[https://homotopy.io][Homotopy.io]] are (awe)inspiring. Do check out his talk titled *Category Theory: Visual Mathematics for the 21st Century* and his works to see how he connects proofs, programs, and geometry together in a triad! + +*** Category Theory: Visual Mathematics for the 21st Century #+BEGIN_HTML +#+END_HTML + +*** Globular.science and Homotopy.io + +#+BEGIN_HTML +
#+END_HTML Now when studying category theory, to start seeing how the pieces fit together one has to recourse to abstract diagrams and attempt to connect these concepts with how the same concepts model things in a more visual domain, say topology. This recourse is my best bet at the moment to gain the geometric intuitions in Category Theory when learning. If you find geometric intuitions helpful in understanding mathematics, let me draw your attention to this incomplete but [[https://boris-marinov.github.io/category-theory-illustrated/][beautiful work]] by Boris Marinov. @@ -194,7 +219,7 @@ https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_ ** [[https://amzn.to/3brrok3][Algebra: Chapter 0]] -** Tangential Reads +** Adjacent Reads Now these are works a bit removed from Category Theory, but still I feel will give one a good understanding of the big picture if put in the effort to understand these: