Definable Categorical Equivalence

Laurenz Hudetz

doi:10.1086/701047

Erratum: “A categorical equivalence between generalized holonomy maps on a connected manifold and principal connections on bundles over that manifold” [J. Math. Phys. 57, 102902 (2016)]

Journal of Mathematical Physics ◽

10.1063/1.5019748 ◽

2018 ◽

Vol 59 (2) ◽

pp. 029901

Author(s):

Sarita Rosenstock ◽

James Owen Weatherall

Keyword(s):

Categorical Equivalence ◽

Connected Manifold ◽

Math Phys

A categorical equivalence between semi-Heyting algebras and centered semi-Nelson algebras

Logic Journal of IGPL ◽

10.1093/jigpal/jzy006 ◽

2018 ◽

Vol 26 (4) ◽

pp. 408-428 ◽

Cited By ~ 1

Author(s):

Juan Manuel Cornejo ◽

Hernán Javier San Martín

Keyword(s):

Heyting Algebras ◽

Categorical Equivalence ◽

Nelson Algebras

MORITA EQUIVALENCE

The Review of Symbolic Logic ◽

10.1017/s1755020316000186 ◽

2016 ◽

Vol 9 (3) ◽

pp. 556-582 ◽

Cited By ~ 21

Author(s):

THOMAS WILLIAM BARRETT ◽

HANS HALVORSON

Keyword(s):

Morita Equivalence ◽

Categorical Equivalence ◽

Theoretical Equivalence

AbstractLogicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.

Proof of a Conjecture of S. Mac Lane

BRICS Report Series ◽

10.7146/brics.v3i61.18773 ◽

1996 ◽

Vol 3 (61) ◽

Author(s):

Sergei Soloviev

Keyword(s):

Linear Logic ◽

Sufficient Conditions ◽

Vector Spaces ◽

Categorical Equivalence ◽

Closed Category ◽

Symmetric Monoidal Closed Category ◽

Monoidal Closed Category ◽

Coherence Theorem ◽

Mac Lane

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions (only this case was considered in the original Mac Lane conjecture). Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered (together with categorical equivalence). Two derivations of the same sequent are equivalent if and only if all their interpretations in K are equal. In fact, the assignment of values (objects of K) to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the "abstract coherence theorem" found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture proves also the correctness of the modified description.

Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices

International Journal of Theoretical Physics ◽

10.1007/s10773-017-3433-4 ◽

2017 ◽

Vol 56 (12) ◽

pp. 4060-4072

Author(s):

Kohei Kishida ◽

Soroush Rafiee Rad ◽

Joshua Sack ◽

Shengyang Zhong

Keyword(s):

Orthomodular Lattices ◽

Categorical Equivalence

A Categorical Equivalence Motivated by Kalman’s Construction

Studia Logica ◽

10.1007/s11225-015-9632-1 ◽

2015 ◽

Vol 104 (2) ◽

pp. 185-208

Author(s):

Marta S. Sagastume ◽

Hernán J. San Martín

Keyword(s):

Categorical Equivalence

ℍ-Perfect Pseudo MV-Algebras and Their Representations

Mathematica Slovaca ◽

10.1515/ms-2015-0054 ◽

2015 ◽

Vol 65 (4) ◽

Cited By ~ 3

Author(s):

Anatolij Dvurečenskij

Keyword(s):

Lexicographic Product ◽

Real Numbers ◽

Categorical Equivalence ◽

The Real ◽

Mv Algebras

AbstractWe study ℍ-perfect pseudo MV-algebras, that is, algebras which can be split into a system of ordered slices indexed by the elements of an subgroup ℍ of the group of the real numbers. We show when they can be represented as a lexicographic product of ℍ with some ℓ-group. In addition, we show also a categorical equivalence of this category with the category of ℓ-groups.

Categorical Equivalence and the Renormalization Group

Fortschritte der Physik ◽

10.1002/prop.201910019 ◽

2019 ◽

Vol 67 (8-9) ◽

pp. 1910019

Author(s):

Eric Sharpe

Keyword(s):

Renormalization Group ◽

Categorical Equivalence

Categorical equivalence of algebras with a majority term

Algebra Universalis ◽

10.1007/s000120050087 ◽

1998 ◽

Vol 40 (2) ◽

pp. 149-175 ◽

Cited By ~ 7

Author(s):

C. Bergman

Keyword(s):

Categorical Equivalence ◽

Majority Term

Arithmetical affine complete varieties and inverse monoids

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2007.1040 ◽

2008 ◽

Vol 45 (1) ◽

pp. 13-28 ◽

Cited By ~ 1

Author(s):

Kalle Kaarli

Keyword(s):

Distributive Lattice ◽

Finite Type ◽

Categorical Equivalence ◽

Inverse Monoids ◽

Affine Complete

This paper gives a classification of arithmetical affine complete varieties of finite type up to categorical equivalence. It is proved that two such varieties are equivalent as categories if and only if their weakly diagonal generators have isomorphic monoids of bicongruences. Moreover, it is proved that the monoids appearing in this situation are precisely the inverse factorizable monoids with zero, with distributive lattice of idempotents, and satisfying a certain idempotent-unit condition (IU).