50 papers
This paper develops pivotal and spherical versions of graded extension theory for tensor categories, defining corresponding Brauer-Picard 2-categorical groups, classifying extensions via monoidal 2-functors, and establishing an obstruction theory for extending these structures.
This paper establishes the relationship between pairings of May operads and compatible pairs of indexing systems, demonstrating that operad pairings induce system pairings and that, in many cases, compatible indexing systems can be realized by pairings of -operads.
This paper introduces Calabi--Yau quadruples to demonstrate that their associated Higgs categories are -Calabi--Yau Frobenius extriangulated categories with canonical -cluster-tilting subcategories, thereby proving that both relative Amiot--Guo--Keller and Higgs constructions transform silting reduction into Calabi--Yau reduction.
This paper establishes that the most general "reasonable category of strong vector spaces" admitting formal infinite sums is equivalent to the category of ultrafinite summability spaces, characterizing it as a specific orthogonal subcategory of and analyzing its monoidal closed structures in relation to other categories of topological vector spaces.
This paper establishes the existence of superdecomposable pure-injective modules over Jacobian algebras associated with triangulations of closed surfaces (excluding spheres with four or fewer punctures) by demonstrating the presence of independent pairs of dense chains of pointed modules in non-domestic skew-gentle and (skew) Brauer graph algebras, thereby confirming M. Prest's conjecture for these specific cases.
This paper introduces a general category-theoretic framework for epistemic uncertainty that unifies various imprecise probability theories, models their interrelationships, and demonstrates how both Bayesian updating and possibilistic conditioning emerge as specific instances of a generalized belief updating process based on change of enrichment.
This paper proposes a new formulation of 3-crossed modules equipped with a novel lifting mechanism, proving that they induce quasi-categories and arise naturally from the Moore complex of length 3, thereby establishing a robust foundation for extending the equivalence between higher algebraic structures and Gray 3-groups.
This paper introduces a homological stratification theory for rigidly-compactly generated tensor-triangulated categories, demonstrating its robust descent properties to provide a unified framework for answering when stratification descends and extending equivariant module spectrum results from finite groups to compact Lie groups.
This paper constructs finite-dimensional quantum groups of type Super A at even roots of unity, classifies their ribbon structures to establish non-semisimple modular categories, and demonstrates that the resulting link invariants distinguish knots that are indistinguishable by the Jones or HOMFLYPT polynomials.
This paper corrects mathematical errors in the original theoretical foundation of the UMAP algorithm, provides a self-contained derivation of the underlying functors and metric realization, and clarifies the correspondence between the theoretical framework and the practical UMAP implementation.