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Synthetic Perspectives on Higher StructuresThrough painstaking work, higher structures, such as weak infinite-dimensional categories, can be built "analytically" out of sets. Elaborate formalisms have been developed to ensure that constructions involving these objects are equivalence-invariant. We present an alternate approach using domain-specific formal languages to work with higher structures "synthetically." We argue such formal systems make definitions, theorems, and proofs both easier to understand and easier to formalize. Our contributions to the synthetic theory of higher categories were developed over the course of joint work with Dominic Verity, Mike Shulman, Evan Cavallo, and Christian Sattler, among others.Uploaded 07-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices
