Yes, but then really the statement should be $A \implies B <=> \text{tautology}$, right? Otherwise how else can you say that $A \implies B$ as a total must always be true?
I am perpetually getting through it but it often just feels so irrelevant the things in it for my entire bachelors studium. The book has some pretty deep insight on some matters, but it's hard to keep the motivation up
I think some people may consider it crankery, but I liked it so far. How useful it is, I've yet to figure out. It's hard to apply category than what it was directly made for I think.
It tries to motivate each concept by finding a real life use case, and also at the end of each chapter, it shows how there are traces of a given concept independently in philosophical circles
There is this book called Sheaf Theory by Daniel Rosiak. Now, I confess I have no idea what a sheaf is still, but that book does a damn good job of motivating why categorical ideas are quite natural