/sci/ - Science & Math » Thread #13275013

26KiB, 1200x768, 1200px-Universal_property_of_product.svg.png

View Same Google iqdb SauceNAO

Anonymous Sun 13 Jun 23:26:12 2021 No.13275013 View Reply Original Report

Quoted By: >>13275226 >>13275245

Was category theory meant to be an alternative to set theory ?

From the few things I know about it, it seems to rely on it, it isn't ?

Anonymous

Anonymous Mon 14 Jun 2021 00:29:14 No.13275226 Report

Quoted By:

>>13275013
no, category theory was developed when people studied algebraic topology and is used to study abstract (algebraic) structures in general.

i think it can be used as a foundation, but i dont know enough about to say anything regarding it.

Anonymous

Anonymous Mon 14 Jun 2021 00:35:45 No.13275245 Report

Quoted By:

>>13275013
https://www.youtube.com/watch?v=gVI9fh6RXMY

Anonymous

Anonymous Mon 14 Jun 2021 02:58:33 No.13275651 Report

Quoted By:

No. It’s not an alternative. You can’t do category theory without some notion of set/class.
But using the language of category theory you can write the axioms of set theory in a much more compact way. Look up ETCS which stands for the elementary theory of the category of sets.

Anonymous

View Same Google iqdb SauceNAO 1622153745856.jpg, 288KiB, 1200x853

Anonymous Mon 14 Jun 2021 03:14:31 No.13275684 Report

Quoted By: >>13275935

Algebraic topology is full of jumping from spaces to groups etc. The point of category theory was to develop a proper way to move from one setting to the other. People came up with different ways to do that and noticed that some properties are preserved and some are not. Why is that? Well, that's what they wanted to find out. The foundation clownery came in later.

Anonymous

Anonymous Mon 14 Jun 2021 05:03:14 No.13275935 Report

Quoted By: >>13276245

>>13275684
False like all your worthless posts

Anonymous

Anonymous Mon 14 Jun 2021 06:55:41 No.13276245 Report

Quoted By:

>>13275935
That's not nice.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches