Path Categories and Propositional Identity Types
نویسندگان
چکیده
منابع مشابه
Propositional equality, identity types, and direct computational paths
In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such as, e.g., change of bound variables). When setting up a proof theory for equality one is faced with a rather unexpected situation where there may not be a unique canonical proof of an equality stateme...
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In two early papers, Max Cresswell constructed two formal logics of propositional identity, and , which he observed to be respectively deductively equivalent to modal logics 4 and 5. Cresswell argued informally that these equivalences respectively “give . . . evidence” for the correctness of 4 and 5 as logics of broadly logical necessity. In this paper, I describe weaker propositiona...
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The path category P (X) of a simplicial set X defines a functor X 7→ P (X) which is left adjoint to the nerve functor B : cat → sSet. The first section of this paper contains an elementary description of this functor, with some of its basic properties. This construction specializes to a path category functor for cubical sets which appears in the second section. The path category construction is...
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ژورنال
عنوان ژورنال: ACM Transactions on Computational Logic
سال: 2018
ISSN: 1529-3785,1557-945X
DOI: 10.1145/3204492