publication . Preprint . 2020

Comprehension and quotient structures in the language of 2-categories

Melliès, Paul-André; Rolland, Nicolas;
Open Access English
  • Published: 20 May 2020
Abstract
Lawvere observed in his celebrated work on hyperdoctrines that the set-theoretic schema of comprehension can be elegantly expressed in the functorial language of categorical logic, as a comprehension structure on the functor $p:\mathscr{E}\to\mathscr{B}$ defining the hyperdoctrine. In this paper, we formulate and study a strictly ordered hierarchy of three notions of comprehension structure on a given functor $p:\mathscr{E}\to\mathscr{B}$, which we call (i) comprehension structure, (ii) comprehension structure with section, and (iii) comprehension structure with image. Our approach is 2-categorical and we thus formulate the three levels of comprehension structur...
Subjects
free text keywords: Mathematics - Category Theory, Computer Science - Logic in Computer Science
Funded by
EC| DuaLL
Project
DuaLL
Duality in Formal Languages and Logic - a unifying approach to complexity and semantics
  • Funder: European Commission (EC)
  • Project Code: 670624
  • Funding stream: H2020 | ERC | ERC-ADG
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