Zobrazeno 1 - 10
of 236
pro vyhledávání: '"18A05"'
Effective descent morphisms, originally defined in Grothendieck descent theory, form a class of special morphisms within a category. Essentially, an effective descent morphism enables bundles over its codomain to be fully described as bundles over it
Externí odkaz:
http://arxiv.org/abs/2410.22876
Autor:
Hu, Dongdong
We define the preprojective algebra of a finite EI quiver. We prove that it is isomorphic to a centain tensor algebra. For a finite EI quiver of Cartan type, we prove that the corresponding preprojective algebra is isomorphic to the generalized prepr
Externí odkaz:
http://arxiv.org/abs/2410.15390
Autor:
Perrone, Paolo
The arrows of a category are elements of particular sets, the hom-sets. These sets are functorial, and their functoriality specifies how to compose the arrows with other arrows of the same category. In particular, it allows to form diagrams, making m
Externí odkaz:
http://arxiv.org/abs/2410.08019
Autor:
Vigneaux, Juan Pablo
We use Cramer's formula for the inverse of a matrix and a combinatorial expression for the determinant in terms of paths of an associated digraph (which can be traced back to Coates) to give a combinatorial interpretation of M\"obius inversion whenev
Externí odkaz:
http://arxiv.org/abs/2407.14647
Autor:
Quinn, Frank
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what is, or isn't
Externí odkaz:
http://arxiv.org/abs/2407.02507
Publikováno v:
Theory Appl. Categ. 41(16):516-530, 2024
We investigate the properties of lax comma categories over a base category $X$, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from $\mathsf{Cat}//X$ to $\mathsf{Cat}$ is topological
Externí odkaz:
http://arxiv.org/abs/2405.03773
Autor:
Fomatati, Yves Baudelaire
Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ and $S=$ $K[y_{1},y_{2},\cdots, y_{m}]$ where $K$ is a field. %commutative ring with unity. In this paper, we propose a method showing how to obtain $3$-matrix factors for a given polynomial using either the Dooli
Externí odkaz:
http://arxiv.org/abs/2402.00991
Autor:
Das, Suddhasattwa
The purpose of category theory is to provide a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of th
Externí odkaz:
http://arxiv.org/abs/2401.14059
Autor:
Tuyéras, Rémy
This paper redefines the foundations of asymmetric cryptography's homomorphic cryptosystems through the application of the Yoneda Lemma. It explicitly illustrates that widely adopted systems, including ElGamal, RSA, Benaloh, Regev's LWE, and NTRUEncr
Externí odkaz:
http://arxiv.org/abs/2401.13255
Autor:
Kaipel, Maximilian
In this paper, we introduce the notion of an admissible partition of a simplicial polyhedral fan and define the category of a partitioned fan as a generalisation of the $\tau$-cluster morphism category of a finite-dimensional algebra. This establishe
Externí odkaz:
http://arxiv.org/abs/2311.05444