Results 101 to 110 of about 1,642,029 (305)
Variation on a comprehensive theme [PDF]
arXiv, 2021 The main result concerns a bicategorical factorization system on the bicategory $\mathrm{Cat}$ of categories and functors. Each functor $A\xra{f} B$ factors up to isomorphism as $A\xra{j}E\xra{p}B$ where $j$ is what we call an ultimate functor and $p$ is what we call a groupoid fibration. Every right adjoint functor is ultimate. Functors whose ultimate
arxiv
Counting integral points on symmetric varieties with applications to arithmetic statistics
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract In this article, we combine Bhargava's geometry‐of‐numbers methods with the dynamical point‐counting methods of Eskin–McMullen and Benoist–Oh to develop a new technique for counting integral points on symmetric varieties lying within fundamental domains for coregular representations.
Arul Shankar +2 more
wiley +1 more source
Underlying functors on fibered manifolds
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2004 For a product preserving bundle functor on the category of fibered manifolds we describe subordinated functors and we introduce the concept of the underlying functor. We also show that there is an affine bundle structure on product preserving functors on
Miroslav Doupovec
doaj
Determinant functors on triangulated categories [PDF]
Journal of K-Theory, 2010 AbstractWe study determinant functors which are defined on a triangulated category and take values in a Picard category. The two main results are the existence of a universal determinant functor for every small triangulated category, and a comparison theorem for determinant functors on a triangulated category with a non-degenerate bounded t-structure ...
openaire +3 more sources
From the conformal anomaly to the Virasoro algebra
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract The conformal anomaly and the Virasoro algebra are fundamental aspects of two‐dimensional conformal field theory and conformally covariant models in planar random geometry. In this article, we explicitly derive the Virasoro algebra from an axiomatization of the conformal anomaly in terms of real determinant lines, one‐dimensional vector spaces
Sid Maibach, Eveliina Peltola
wiley +1 more source
Some useful structures for categorical approach for program behavior
Journal of Information and Organizational Sciences, 2011 Using of category theory in computer science has extremely grown in the last decade. Categories allow us to express mathematical structures in unified way. Algebras are used for constructing basic structures used in computer programs.
Viliam Slodičák
doaj
A remark on Yoneda's Lemma [PDF]
arXiv, 2017 Yoneda'e Lemma is about the canonical isomorphism of all the natural transformations from a given representable covariant (contravariant, reps.) functor (from a locally small category to the category of sets) to a covariant (contravariant, reps.) functor.
arxiv
On linearization and uniqueness of preduals
Mathematische Nachrichten, Volume 298, Issue 3, Page 955-975, March 2025.Abstract We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar‐valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space F(Ω)$\mathcal {F}(\Omega)$ of scalar‐valued functions on a nonempty set Ω$\Omega$ is said to admit a strong linearization if there are a ...
Karsten Kruse
wiley +1 more source
Mackey functors on compact closed categories [PDF]
arXiv, 2007 We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey functors on $\E$. We show that it is a monoidal category and the monoids are Green functors.
arxiv
Affine Non‐Reductive GIT and moduli of representations of quivers with multiplicities
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non‐Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original action.
Eloise Hamilton +2 more
wiley +1 more source