Results 81 to 90 of about 20,804 (234)

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, Tobias Lenz, Sil Linskens   +2 more
wiley   +1 more source

Global Dimension of Polynomial Rings in Partially Commuting Variables

, 2008
For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts.
A.A. Husainov, A.A. Husainov, A.A. Husainov, A.A. Khusainov, A.A. Khusainov, A.A. Khusainov, Ahmet A. Husainov, B. Mitchell, B. Mitchell, B. Mitchell, B. Mitchell, C.A. Weibel, H.-J. Baues, J. Leech, L.Y. Polyakova, N. Bourbaki, P. Gabriel, S. Mac Lane, U. Oberst, V. Diekert, V. Diekert   +20 more
core   +2 more sources

The six operations in topology

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract In this paper, we show that the six functor formalism for sheaves on locally compact Hausdorff topological spaces, as developed, for example,‐ in Kashiwara and Schapira's book Sheaves on Manifolds, can be extended to sheaves with values in any closed symmetric monoidal ∞$\infty$‐category which is stable and bicomplete. Notice that, since we do
Marco Volpe
wiley   +1 more source

Structure theorems for braided Hopf algebras

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley   +1 more source

On Endomorphism Universality of Sparse Graph Classes

Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.
ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
wiley   +1 more source

Pathological computations of Mackey functor‐valued Tor over cyclic groups

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3024-3036, October 2025.
Abstract In equivariant algebra, Mackey functors play the role of abelian groups and Green and Tambara functors play the role of commutative rings. In this paper, we compute Mackey functor‐valued Tor over certain free Green and Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator.
David Mehrle, J. D. Quigley, Michael Stahlhauer   +2 more
wiley   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

Equations over free inverse monoids with idempotent variables

, 2015
We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a ...
A Jeż, AA Lorents, BV Rozenblat, ChH Papadimitriou, D Bormotov, F Baader, GS Makanin, GS Makanin, HE Scheiblich, KI Appel, M Petrich, T Deis, V Diekert, V Diekert, W Plandowski, WD Munn   +15 more
core   +1 more source

Construction of Bernstein‐Based Words and Their Patterns

Mathematical Methods in the Applied Sciences, Volume 48, Issue 13, Page 12819-12836, September 2025.
ABSTRACT In this paper, with inspiration of the definition of Bernstein basis functions and their recurrence relation, we give construction of a new word family that we refer Bernstein‐based words. By classifying these special words as the first and second kinds, we investigate their some fundamental properties involving periodicity and symmetricity ...
Irem Kucukoglu, Yilmaz Simsek
wiley   +1 more source

Nonsymmetric Askey–Wilson Shift Operators

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We classify the shift operators for the symmetric Askey–Wilson polynomials and construct shift operators for the nonsymmetric Askey–Wilson polynomials using two decompositions of nonsymmetric Askey–Wilson polynomials in terms of symmetric ones. These shift operators are difference–reflection operators, and we discuss the conditions under which
Max van Horssen, Philip Schlösser
wiley   +1 more source