[wesselbindt]

> Surely if the technique is so powerful, there ought to be easy examples of it aplenty

Some examples of insanely powerful and ubiquitous concepts which do not have easy examples:

- algebraic stacks

- QFT

- _general_ relativity

There's this idea that everything should somehow be explainable to my grandmother, but this idea is never presented with any justification, and it seems to me that there's counterexamples aplenty. And something irks me about the idea. I feel like it comes from the same place as people who've done a 5 minute search on google feeling like they can take on experts who've spent decades studying a subject.

[cirpis]

This seems like a needlesly defensive answer. If there are no examples then just say so. It is mathematics after all, some of it is beautiful to explore just for its own sake, no examples or applications neccesary.

But claiming a technique is a bridge between disparate areas of mathematics and then subsequently failing to give concrete examples of such bridging is a bit odd, dont you think?

For what its worth the book "7 sketches in compositionality" (https://arxiv.org/abs/1803.05316) has a chapter on topos theory which provides a good introduction with some simple examples!