The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
Caterina Consani - One of the best experts on this subject based on the ideXlab platform.
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Cyclic structures and the topos of simplicial sets
Journal of Pure and Applied Algebra, 2015Co-Authors: Alain Connes, Caterina ConsaniAbstract:Abstract Given a point p of the topos Δ ˆ of simplicial sets and the corresponding flat Covariant Functor F : Δ ⟶ Sets , we determine the extensions of F to the cyclic category Λ ⊃ Δ . We show that to each such cyclic structure on a point p of Δ ˆ corresponds a group G p , that such groups can be noncommutative and that each G p is described as the quotient of a left-ordered group by the subgroup generated by a central element. Moreover for any cyclic set X the fiber (or geometric realization) of the underlying simplicial set of X at p inherits canonically the structure of a G p -space. This gives a far reaching generalization of the well-known circle action on the geometric realization of cyclic sets.
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Cyclic structures and the topos of simplicial sets
arXiv: Algebraic Geometry, 2013Co-Authors: Alain Connes, Caterina ConsaniAbstract:Given a point p of the topos of simplicial sets and the corresponding flat Covariant Functor F from the small category Delta to the category of sets, we determine the extensions of F to the cyclic category. We show that to each such cyclic structure on a point p of the topos of simplicial sets corresponds a group G(p), that such groups can be noncommutative and that each G(p) is described as the quotient of a left-ordered group by the subgroup generated by a central element. Moreover for any cyclic set X, the fiber (or geometric realization) of the underlying simplicial set of X at p inherits canonically the structure of a G(p)-space. This gives a far reaching generalization of the well-known circle action on the geometric realization of cyclic sets.
Alain Connes - One of the best experts on this subject based on the ideXlab platform.
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Cyclic structures and the topos of simplicial sets
Journal of Pure and Applied Algebra, 2015Co-Authors: Alain Connes, Caterina ConsaniAbstract:Abstract Given a point p of the topos Δ ˆ of simplicial sets and the corresponding flat Covariant Functor F : Δ ⟶ Sets , we determine the extensions of F to the cyclic category Λ ⊃ Δ . We show that to each such cyclic structure on a point p of Δ ˆ corresponds a group G p , that such groups can be noncommutative and that each G p is described as the quotient of a left-ordered group by the subgroup generated by a central element. Moreover for any cyclic set X the fiber (or geometric realization) of the underlying simplicial set of X at p inherits canonically the structure of a G p -space. This gives a far reaching generalization of the well-known circle action on the geometric realization of cyclic sets.
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Cyclic structures and the topos of simplicial sets
arXiv: Algebraic Geometry, 2013Co-Authors: Alain Connes, Caterina ConsaniAbstract:Given a point p of the topos of simplicial sets and the corresponding flat Covariant Functor F from the small category Delta to the category of sets, we determine the extensions of F to the cyclic category. We show that to each such cyclic structure on a point p of the topos of simplicial sets corresponds a group G(p), that such groups can be noncommutative and that each G(p) is described as the quotient of a left-ordered group by the subgroup generated by a central element. Moreover for any cyclic set X, the fiber (or geometric realization) of the underlying simplicial set of X at p inherits canonically the structure of a G(p)-space. This gives a far reaching generalization of the well-known circle action on the geometric realization of cyclic sets.
Sri Wahyuni - One of the best experts on this subject based on the ideXlab platform.
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fungtorialitas dan isomorfisma aljabar insidensisuatu partially ordered set poset
2011Co-Authors: Sri WahyuniAbstract:In forming a Functor from category of poset to category of algebra, a relation of object and morphism on these categories is needed. Category of incidence algebra is a part of category of algebra. From the poset and commutative ring can be formed an incidence algebra. In general, a morphism on category of poset does not induce morphism on incidence algebra. This implies that the Functor formed is not well-generated. There are two methods that have been done to make it running well, first is to define a bimodule on incidence algebra that functioned as the morphism, and second to restrict the poset so that it works on simplicial complexes. In this disertation a new Functor is generated: a Functor from category of poset to category of simplicial complexes. This is made in order to get a Functor from the category of Poset to the category of algebra by using Functor composition. In general incidence algebra is defined on locally finite poset so that the multiplicative operation is well-defined. In this disertation, a new definition of incidence algebra is defined on an abritarary poset, but with an additional requirement, that is the finite of its sub poset, so that the incidence algebra can be defined, called finitary incidence algebra. With this new definition, it is found that a Covariant Functor from category of poset to incidence algebra is obtained, and some isomorphism problems on finitary incidence algebra can be solved by applying this definition. In particular, for potentially isomorphic problem, there must be some additional requirement on one of the poset. Covariant Functor can be found from the category of simplicial complexes to the category of abelian groups. The Functor is simplicial chain group, which is the sequence of them will form a simplicial chain complex. Morphism which assign simplicial chain complex is simplicial chain map, and finally the new category called category of simplicial chain complex can be obtained.
Almira Latipova - One of the best experts on this subject based on the ideXlab platform.
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some properties of the Covariant Functor set of exponential type
Revista Gestão Inovação e Tecnologias, 2021Co-Authors: Tursunbay Zhuraev, Alisher Umarov, Kamariddin Zhuvonov, Almira LatipovaAbstract:In this paper, it is shown that the sets of all non-empty subsets Set (x) of a topological space X with exponential topology is a Covariant Functor in the category of -topological spaces and their continuous mappings into itself. It is shown that the Functor Set is a Covariant Functor in the category of topological spaces and continuous mappings into itself, a pseudometric in the space Set (x) is defined, and compact, connected, finite, and countable subspaces of Set (x) are distinguished. It also shows various kinds of connectivity, soft, locally soft, and n - soft mappings in Set (x). One interesting example is given for the TOPY category. It is proved that the Functor Set maps open mappings to open, contractible and locally contractible spaces and into contractible and locally contractible spaces.
K P Shum - One of the best experts on this subject based on the ideXlab platform.
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Covariant Functor of soft γ hyperrings
Asian-european Journal of Mathematics, 2020Co-Authors: S Ostadhadidehkordi, K P ShumAbstract:It is known that a soft Γ-hyperring is a generalization of soft ring. The concept of soft Γ-hyperring was first introduced by Zhan et al. In fact, Zhan et al. also established three isomorphism the...
