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computational trilogy in nLab

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computational trinitarianism = propositions as types +programs as proofs +relation type theory/category theory homotopy levels type theory 2-type theory, 2-categorical logic homotopy type theory, homotopy type theory - contents homotopy type univalence, function extensionality, internal logic of an (∞,1)-topos cohesive homotopy type theory directed homotopy type theory HoTT methods for homotopy theorists semantics internal logic, categorical semantics internal logic of a topos Mitchell-Benabou language Kripke-Joyal semantics internal logic of an (∞,1)-topos Edit this sidebar category theory category functor natural transformation Cat universal construction representable functor adjoint functor limit/colimit weighted limit end/coend Kan extension Yoneda lemma Isbell duality Grothendieck construction adjoint functor theorem monadicity theorem adjoint lifting theorem Tannaka duality Gabriel-Ulmer duality small object argument Freyd-Mitchell embedding theorem relation between type theo

computational trilogy in nLab nLab computational trilogy Skip the Navigation Links | Home Page | All Pages | Latest Revisions | Discuss this page | Contents Context Type theory natural deduction metalanguage , practical foundations judgement hypothetical judgement , sequent antecedents ⊢ \vdash consequent , succedents type formation rule term introduction rule term elimination rule computation rule type theory ( dependent , intensional , observational type theory , homotopy type theory ) calculus of constructions syntax object language theory , axiom proposition / type ( propositions as types

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