scholarly journals Categorical equivalence of algebras with a majority term

1998 ◽  
Vol 40 (2) ◽  
pp. 149-175 ◽  
Author(s):  
C. Bergman
Keyword(s):  
Categorical Equivalence ◽  
Majority Term

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

2018 ◽  
Vol 26 (4) ◽  
pp. 408-428 ◽  
Author(s):  
Juan Manuel Cornejo ◽  
Hernán Javier San Martín
Keyword(s):  
Heyting Algebras ◽  
Categorical Equivalence ◽  
Nelson Algebras

scholarly journals MORITA EQUIVALENCE

2016 ◽  
Vol 9 (3) ◽  
pp. 556-582 ◽  
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.

scholarly journals Proof of a Conjecture of S. Mac Lane

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.

scholarly journals Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices

2017 ◽  
Vol 56 (12) ◽  
pp. 4060-4072
Author(s):  
Kohei Kishida ◽  
Soroush Rafiee Rad ◽  
Joshua Sack ◽  
Shengyang Zhong
Keyword(s):  
Orthomodular Lattices ◽  
Categorical Equivalence

Subalgebras of the squares of weakly diagonal majority algebras

2012 ◽  
Vol 49 (4) ◽  
pp. 509-524
Author(s):  
Kalle Kaarli
Keyword(s):  
Natural Structure ◽  
Majority Term ◽  
Minimal Algebra

If A is a minimal algebra (that is, has no proper subalgebras) then the set S2(A) of all subalgebras of A2 has a natural structure of ordered involutive monoid. This paper gives a characterization of monoids S that appear in the role of this monoid if A is finite, weakly diagonal (every subalgebra of A2 contains the graph of an automorphism of A) and has a majority term.

scholarly journals Definable Categorical Equivalence

2019 ◽  
Vol 86 (1) ◽  
pp. 47-75 ◽  
Author(s):  
Laurenz Hudetz
Keyword(s):  
Categorical Equivalence

scholarly journals A Categorical Equivalence Motivated by Kalman’s Construction

Studia Logica ◽  
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

2015 ◽  
Vol 65 (4) ◽  
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.

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