On categorical semantics for type theories and presenting a solution to the initiality conjecture for type theories formulated in terms of second-order generalized algebraic theories:
Taichi Uemura, A General Framework for the Semantics of Type Theory [arXiv:1904.04097, talk slides: pdf]
Taichi Uemura, Abstract and concrete type theories, PhD thesis (2021) [hdl:11245.1/41ff0b60-64d4-4003-8182-c244a9afab3b, pdf]
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