Thierry Coquand on Computational Interpretation of Topos Theory

See Stefan Milius - Demystifying Codensity Monads through Duality and Terence Tao Formalising Riemann-Stieltjes Integrals in Lean Mathlib. 

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53:29 He describes a type theory as a living object, programmed in some language [and running on computers.] 

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This talk by Steve Awodey was given in December 2010

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See the list of the 4th Huawei IHES workshop talks here. This is the one by Olivia Caramello on Grothendieck Toposes in Mathematics: 

8:22 See Morita equivalence in nlab. Also more on finitary models at 35:50 and 45:08. See also Wiesław Kubiś - Generic Mathematical Structures. 

See the Toposes in Como 2018 talks here. See also these posts of mine: Alain Connes on Toposes and Integers and Terence Tao - Using Claude, ChatGPT to Formalise A Theorem About Magmas in Lean. 

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