You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
In many fields, it’s common to publish a review article, which attempts to collect information comprehensively about the current state of a field, especially an active one with lots of new research spread out across different sub-topics.
Do mathematicians do literature reviews?
If you wanted to do a casual one yourself, which database should you search in? MathSciNet? I think you need a university login for that one. https://www.ams.org/publications/math-reviews/math-reviews
Example use case: get an overview of all the different fields topos theory is finding applications in, from physics to logic to non-mathematical disciplines.
They exist, but mathematicians tend to put a lot more effort into depth rather than breadth. They're typically called "surveys", which have been alluded to in another topic recently... oh and also one that you're involved in @Julius Hamilton . For applications of a given thing, you might want to look into history of mathematics surveys?