scholarly journals A categorical equivalence between generalized holonomy maps on a connected manifold and principal connections on bundles over that manifold

2016 ◽  
Vol 57 (10) ◽  
pp. 102902 ◽  
Author(s):  
Sarita Rosenstock ◽  
James Owen Weatherall
Keyword(s):  
Categorical Equivalence ◽  
Connected Manifold

scholarly journals Projective Connections and Projective Transformations

1957 ◽  
Vol 12 ◽  
pp. 1-24 ◽  
Author(s):  
Noboru Tanaka
Keyword(s):  
Affine Transformations ◽  
Connected Manifold ◽  
Projective Transformations

The main purpose of the present paper is to establish a theorem concerning the relation between the group of all projective transformations on an affinely connected manifold and the group of all affine transformations.

scholarly journals Yang–Mills theory and jumping curves

2015 ◽  
Vol 26 (05) ◽  
pp. 1550029
Author(s):  
Yasha Savelyev
Keyword(s):  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Chain Complex ◽  
Complex Manifolds ◽  
Smooth Manifolds ◽  
Hermitian Vector Bundle ◽  
Connected Manifold ◽  
Classical Sense ◽  
Yang Mills ◽  
Simply Connected

We study a smooth analogue of jumping curves of a holomorphic vector bundle, and use Yang–Mills theory over S2 to show that any non-trivial, smooth Hermitian vector bundle E over a smooth simply connected manifold, must have such curves. This is used to give new examples complex manifolds for which a non-trivial holomorphic vector bundle must have jumping curves in the classical sense (when c1(E) is zero). We also use this to give a new proof of a theorem of Gromov on the norm of curvature of unitary connections, and make the theorem slightly sharper. Lastly we define a sequence of new non-trivial integer invariants of smooth manifolds, connected to this theory of smooth jumping curves, and make some computations of these invariants. Our methods include an application of the recently developed Morse–Bott chain complex for the Yang–Mills functional over S2.

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.

Local cohomology of the algebra of C ∞ functions on a connected manifold

1980 ◽  
Vol 4 (3) ◽  
pp. 157-167 ◽  
Author(s):  
M. Cahen ◽  
S. Gutt ◽  
M. De Wilde
Keyword(s):  
Local Cohomology ◽  
Connected Manifold

scholarly journals In simply connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiro Lee Tanaka
Keyword(s):  
Connected Manifold ◽  
Cotangent Bundles ◽  
Lagrangian Cobordisms ◽  
Simply Connected ◽  
Lagrangian Cobordism

Abstract Let Q be a simply connected manifold. We show that every exact Lagrangian cobordism between compact, exact Lagrangians in T*Q is an h-cobordism. This is a corollary of the Abouzaid–Kragh Theorem.

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
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