On Doctrines and Cartesian Bicategories

06/15/2021
by   Filippo Bonchi, et al.
0

We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in algebraic terms based on a string diagrammatic calculus, the latter in universal terms using the fundamental notion of adjoint functor. We prove that these two approaches are related by an adjunction, which can be strengthened to an equivalence by imposing further constraints on doctrines.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 3

page 9

page 15

page 17

10/13/2021

Representing Matrices Using Algebraic ZX-calculus

Elementary matrices play an important role in linear algebra application...
02/10/2021

Elementary equivalence versus isomorphism in semiring semantics

We study the first-order axiomatisability of finite semiring interpretat...
01/22/2020

Profunctor optics and traversals

Optics are bidirectional accessors of data structures; they provide a po...
10/21/2019

Parametrized Complexity of Expansion Height

Deciding whether two simplicial complexes are homotopy equivalent is a f...
02/19/2019

Elementary-base cirquent calculus II: Choice quantifiers

Cirquent calculus is a novel proof theory permitting component-sharing b...
04/03/2018

The Logical Essentials of Bayesian Reasoning

This chapter offers an accessible introduction to the channel-based appr...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.