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pro vyhledávání: '"Awodey, Steve"'
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber cate
Externí odkaz:
http://arxiv.org/abs/2406.18497
Autor:
Awodey, Steve
The category of Cartesian cubical sets is introduced and endowed with a Quillen model structure using ideas coming from recent constructions of cubical systems of univalent type theory.
Comment: 104 pages
Comment: 104 pages
Externí odkaz:
http://arxiv.org/abs/2305.00893
Autor:
Awodey, Steve
We have another look at the construction by Hofmann and Streicher of a universe $(U,{\mathsf{E}l})$ for the interpretation of Martin-L\"of type theory in a presheaf category $\psh{\C}$. It turns out that $(U,{\mathsf{E}l})$ can be described as the \e
Externí odkaz:
http://arxiv.org/abs/2205.10917
Autor:
Awodey, Steve
The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness theorems. This
Externí odkaz:
http://arxiv.org/abs/2001.09195
Akademický článek
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Akademický článek
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Postulating an impredicative universe in dependent type theory allows System F style encodings of finitary inductive types, but these fail to satisfy the relevant {\eta}-equalities and consequently do not admit dependent eliminators. To recover {\eta
Externí odkaz:
http://arxiv.org/abs/1802.02820
Autor:
Awodey, Steve, Newstead, Clive
We assemble polynomials in a locally cartesian closed category into a tricategory, allowing us to define the notion of a polynomial pseudomonad and polynomial pseudoalgebra. Working in the context of natural models of type theory, we prove that depen
Externí odkaz:
http://arxiv.org/abs/1802.00997