Results 11 to 20 of about 391 (50)
A 3‐categorical perspective on G$G$‐crossed braided categories
Journal of the London Mathematical Society, Volume 107, Issue 1, Page 333-406, January 2023., 2023 Abstract A braided monoidal category may be considered a 3‐category with one object and one 1‐morphism. In this paper, we show that, more generally, 3‐categories with one object and 1‐morphisms given by elements of a group G$G$ correspond to G$G$‐crossed braided categories, certain mathematical structures which have emerged as important invariants of ...
Corey Jones +2 more
wiley +1 more source
Digital Hopf Spaces and Their Duals
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this article, we study the fundamental notions of digital Hopf and co‐Hopf spaces based on pointed digital images. We show that a digital Hopf space, a digital associative Hopf space, a digital Hopf group, and a digital commutative Hopf space are unique up to digital homotopy type; that is, there is only one possible digital Hopf structure up to ...
Dae-Woong Lee, Akbar Ali
wiley +1 more source
Towards an M5‐Brane Model II: Metric String Structures
Fortschritte der Physik, Volume 68, Issue 8, August 2020., 2020 Abstract In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six‐dimensional superconformal field theories and we believe that they also underlie potential future formulations of the (2,0)‐theory. We show that the connections on non‐abelian gerbes usually introduced
Christian Sämann, Lennart Schmidt
wiley +1 more source
Algebraic Structures Based on a Classifying Space of a Compact Lie Group
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be
Dae-Woong Lee, Teoman Özer
wiley +1 more source
Some examples of nontrivial homotopy groups of modules
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 3, Page 189-195, 2001., 2001 The concept of the homotopy theory of modules was discovered by Peter Hilton as a result of his trip in 1955 to Warsaw, Poland, to work with Karol Borsuk, and to Zurich, Switzerland, to work with Beno Eckmann. The idea was to produce an analog of homotopy theory in topology.
C. Joanna Su
wiley +1 more source
A new look at means on topological spaces
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 617-620, 1997., 1997 We use methods of algebraic topology to study when a connected topological space admits an n‐mean map.
Peter Hilton
wiley +1 more source
Parametrized stability and the universal property of global spectra
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract We develop a framework of parametrized semiadditivity and stability with respect to so‐called atomic orbital subcategories of an indexing ∞$\infty$‐category T$T$, extending work of Nardin. Specializing this framework, we introduce global ∞$\infty$‐categories and the notions of equivariant semiadditivity and stability, yielding a higher ...
Bastiaan Cnossen +2 more
wiley +1 more source
, 2013 We prove that a separable Hausdorff topological space $X$ containing a cocountable subset homeomorphic to $[0,\omega_1]$ admits no separately continuous mean operation and no diagonally continuous $n$-mean for $n\ge 2$.Comment: 6 ...
Banakh, Taras +2 more
core +3 more sources
Operads within monoidal pseudo algebras
, 2004 A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra.
Weber, Mark
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Finite generation of Tate cohomology of symmetric Hopf algebras [PDF]
, 2013 Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$.
Nguyen, Van C.
core