I often hear that category theory (and/or homotopy type theory) can serve as an alternative to set theory as a foundation for mathematical thinking.
How mainstream is this idea among mathematicians and philosophers of mathematics?
Perhaps @johncarlosbaez can weigh in?
@DrYohanJohn @johncarlosbaez not directly an answer to your question but relevant:
Awodey's From sets to types to categories to sets
Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby.
https://kilthub.cmu.edu/articles/journal_contribution/From_Sets_to_Types_to_Categories_to_Sets/6491651
@rrrichardzach @johncarlosbaez
Thanks! I've read some of Awodey's papers... I'll definitely have a look.
Yohan John 🤖🧠
Richard Zach