@Anthony_Bonato Is category theory actually useful for anything? I’ve found it to be impenetrably esoteric. The only parts of it I can actually understand are extremely obvious. Am I missing something?

@Anthony_Bonato For whom it is being simplified is not stated.

@Anthony_Bonato woahhh

@Anthony_Bonato Yes! As things get simplified, they also get condensed. To express the same content with equations and sentences, you might need a page or two and not be more enlightened at the end. Same effect that makes algebraic notation express pithily what took clumsy paragraphs before.

@Anthony_Bonato Kind of the opposite is true....

@Anthony_Bonato is this a principle G-bundle with \lambda_g the action on the total space?

@Anthony_Bonato I think if you’re looking at something specific like principal fiber bundles you’re not *really* doing category theory anyway. You’re just looking at an example.

@Anthony_Bonato Is this sarcasm? If so, I think it’s misplaced — how would you simply express the information here without a commutative diagram?

@Anthony_Bonato This isn’t even category theory it’s just a diagram

@Anthony_Bonato Clearly it's failing, as you diagram confusingly, unfathomably illustrates! :)

@Anthony_Bonato Which pathways are exact?

@Anthony_Bonato

@Anthony_Bonato

@Anthony_Bonato Certainly, it will take some hours and a truly effort to explain the meaning behind this picture with other math theories.

@Anthony_Bonato @sudqijawabreh 😂😂

@Anthony_Bonato One of the most memorable talks I have l l attended was by a postdoc at AIS whose main result was the equivalence of two categories. The talk was 45 mins and 35 of them were dedicated to proving that the map he introduced was well-defined.

@Anthony_Bonato When will they release higher dimensional topologically complex commutative diagrams 🙄

@Anthony_Bonato 😀

@Anthony_Bonato Pls kill me

@Anthony_Bonato Simplifying things is hard work