DeepAI AI Chat

Morita equivalences between algebraic dependent type theories

04/13/2018

∙

by Valery Isaev, et al.

∙

∙

We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of models of a type theory often carries a natural structure of a model category. If this holds for the categories of models of two theories, then a map between them is a Morita equivalence if and only if the adjunction generated by it is a Quillen equivalence.

page 1

page 2

page 3

page 4

∙ 02/17/2020

Graded Algebraic Theories

We provide graded extensions of algebraic theories and Lawvere theories ...

0 Satoshi Kura, et al. ∙

∙ 03/09/2023

A conservativity result for homotopy elementary types in dependent type theory

We prove a conservativity result for extensional type theories over prop...

0 Matteo Spadetto, et al. ∙

∙ 11/14/2022

External univalence for second-order generalized algebraic theories

Voevodsky's univalence axiom is often motivated as a realization of the ...

0 Rafaël Bocquet, et al. ∙

∙ 02/22/2019

On Nominal Syntax and Permutation Fixed Points

We propose a new axiomatisation of the alpha-equivalence relation for no...

0 Mauricio Ayala-Rincón, et al. ∙

∙ 03/27/2013

On Some Equivalence Relations between Incidence Calculus and Dempster-Shafer Theory of Evidence

Incidence Calculus and Dempster-Shafer Theory of Evidence are both theor...

0 F. Correa da Silva, et al. ∙

∙ 02/14/2020

Abstract rewriting internalized

In traditional rewriting theory, one studies a set of terms up to a set ...

0 Maxime Lucas, et al. ∙

∙ 02/22/2021

Polymorphic Automorphisms and the Picard Group

We investigate the concept of definable, or inner, automorphism in the l...

0 Pieter Hofstra, et al. ∙