Year: 2024
Type: preprint
Abstract: We present a type theory called fibrational virtual double type theory (FVDblTT) designed specifically for formal category theory, which is a succinct reformulation of New and Licata's Virtual Equipment Type Theory (VETT). FVDblTT formalizes reasoning on isomorphisms that are commonly employed in category theory. Virtual double categories are one of the most successful frameworks for developing formal category theory, and FVDblTT has them as a theoretical foundation. We validate its worth as an internal language of virtual double categories by providing a syntax-semantics duality between virtual double categories and specifications in FVDblTT as a biadjunction.
Source: arXiv (Cornell University)
Author: Nasu, Hayato
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403345472