
Constructing Initial Algebras Using Inflationary Iteration
An old theorem of Adámek constructs initial algebras for sufficiently co...
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Quotients, inductive types, and quotient inductive types
This paper introduces an expressive class of indexed quotientinductive ...
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Constructing Infinitary QuotientInductive Types
This paper introduces an expressive class of quotientinductive types, c...
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Typal Heterogeneous Equality Types
The usual homogeneous form of equality type in MartinLöf Type Theory co...
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Modal Dependent Type Theory and Dependent Right Adjoints
In recent years we have seen several new models of dependent type theory...
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Models of Type Theory Based on Moore Paths
This paper introduces a new family of models of intensional MartinLöf t...
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Internal Universes in Models of Homotopy Type Theory
We show that universes of fibrations in various models of homotopy type ...
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Decomposing the Univalence Axiom
This paper investigates the univalence axiom in intensional MartinLöf t...
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Axioms for Modelling Cubical Type Theory in a Topos
The homotopical approach to intensional type theory views proofs of equa...
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Andrew M. Pitts
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