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2012

Topological and Simplicial Models of Identity Types

7 years 21 days ago
Topological and Simplicial Models of Identity Types
racting these leads us to introduce the notion of a path object category. This is a relatively simple axiomatic framework, which is nonetheless sufficiently strong to allow the construction of homotopy-theoretic models. Now by exhibiting suitable path object structures on Top and SSet, we endow those categories with the structure of a homotopy-theoretic model: and, in this way, obtain the desired topological and simplicial models of identity types. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic—Lambda calculus and related systems General Terms: Theory Additional Key Words and Phrases: Dependent type theory, Identity types, Categorical semantics, Homotopy theory ACM Reference Format: ACM Trans. Comput. Logic V, N, Article A (January YYYY), 44 pages. DOI = 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000
Benno van den Berg, Richard Garner
Added 29 Sep 2012
Updated 29 Sep 2012
Type Journal
Year 2012
Where TOCL
Authors Benno van den Berg, Richard Garner
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