#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Options

# Introduction: Dennis Yao

in Chat

Hi everyone,

I'm a software developer with a background in philosophy and computer science. I became interested in Category Theory a few years ago because I liked the elegant looking diagrams, but I really became hooked when I understood what a pullback was. My primary references have been Schanuel and Lawvere (2009) and Awodey (2006). My main goal with this course is to build a wider repertoire of examples that I can use to ground my intuitions that have been floating around since I began. I'm also really interested in toposes and categorical logic (I'm not sure if any of that will be covered in the course, but it's fascinating to me).

• Options
1.
edited June 2018

Welcome to the course, Dennis! Where do you live or work, if it's not too nosy to ask?

We will definitely talk a bit about topos theory in the course. Chapter 3 of our textbook Seven Sketches is about databases, treating them as functors from a category to $$\mathbf{Set}$$. The category of all functors from some category to $$\mathbf{Set}$$, and natural transformations between these, is a very nice example of a topos.

Chapter 7 is more explicitly about topos theory: it's titled "Sheaves, toposes and internal languages". This arises from David Spivak's use of topos theory to help redesign the air traffic control system - a project he did with NASA, which unfortunately has not been carried to completion.

(That is, nobody is currently planning to actually specify the behavior of the air traffic control system using the internal language of a topos, even though it could be a good idea.)

Comment Source:Welcome to the course, Dennis! Where do you live or work, if it's not too nosy to ask? We will definitely talk a bit about topos theory in the course. Chapter 3 of our textbook _[Seven Sketches](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf)_ is about databases, treating them as functors from a category to \$$\mathbf{Set}\$$. The category of all functors from some category to \$$\mathbf{Set}\$$, and natural transformations between these, is a very nice example of a topos. Chapter 7 is more explicitly about topos theory: it's titled "Sheaves, toposes and internal languages". This arises from David Spivak's use of topos theory to help redesign the air traffic control system - a project he did with NASA, which unfortunately has not been carried to completion. (That is, nobody is currently planning to actually specify the behavior of the air traffic control system using the internal language of a topos, even though it could be a good idea.) 
• Options
2.

Thanks for the welcome John. I currently live and work in Austin (my BSc is from UT).

I'm excited to learn about the categoric perspective on databases! From what you've said, it sounds like a nice way to grasp what "representable" in representable functor means.

Also, the topos-theoretic air traffic control system sounds amazing.

Comment Source:Thanks for the welcome John. I currently live and work in Austin (my BSc is from UT). I'm excited to learn about the categoric perspective on databases! From what you've said, it sounds like a nice way to grasp what "representable" in representable functor means. Also, the topos-theoretic air traffic control system sounds amazing.