Is the diagram at 30:05 right?
It says: (A+C)x(B+C)=(A+B)xC
However I can't stop thinking it should be: (AxC)+(BxC)=(A+B)xC
Category Theory for the Working Hacker [video]
21–30 of 45 posts
Re: Category Theory for the Working Hacker [video]
#22Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these?
Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion.
Is there a reason for this?
Re: Category Theory for the Working Hacker [video]
#23Is the diagram at 30:05 right? It says: (A+C)x(B+C)=(A+B)xC However I can't stop thinking it should be: (AxC)+(BxC)=(A+B)xC
That's how I learned it in grade school, yup.
Re: Category Theory for the Working Hacker [video]
#24Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these? Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion. Is there a reason for this?
The word function has a sort of precis mening in math as a rule mapping each NUMBER in some domain to some NUMBER in a codomaon. The word arrow however can refer to any directed relation including less than or divides or what not, as long as they are composable and associative
Re: Category Theory for the Working Hacker [video]
#25Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these? Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion. Is there a reason for this?
The word function has a sort of precis mening in math as a rule mapping each NUMBER in some domain to some NUMBER in a codomaon. The word arrow however can refer to any directed relation including less than or divides or what not, as long as they are composable and associative
Further math is sort of a stone age technology
Re: Category Theory for the Working Hacker [video]
#26Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these? Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion. Is there a reason for this?
Functions are one kind of arrow. There are other arrows besides functions.
Renaming "arrow" to "function" is like replacing "number" with "1".
Re: Category Theory for the Working Hacker [video]
#27A nice presentation I found to introduce software engineers to category theory and its areas of application:
http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
I don't know category theory so I can't vet it. My skimming of it did show it was interesting, though.
Re: Category Theory for the Working Hacker [video]
#28This is fantastically timed and very well explained. Our company is working deeply with Category Theory right now as we believe programming in the future will find itself focused primarily on the task of orchestrating AI to code.
Re: Category Theory for the Working Hacker [video]
#29Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these? Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion. Is there a reason for this?
The word function has a sort of precis mening in math as a rule mapping each NUMBER in some domain to some NUMBER in a codomaon. The word arrow however can refer to any directed relation including less than or divides or what not, as long as they are composable and associative
That's not even true. Functions can map between lots of things, not necessarily numbers.
Re: Category Theory for the Working Hacker [video]
#30Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these? Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion. Is there a reason for this?
Functions are one kind of arrow. There are other arrows besides functions. Renaming "arrow" to "function" is like replacing "number" with "1".
What other types of arrows are there?