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T 2 and T 3 objects at p in the category of proximity spaces

Muammer Kula, Samed Özkan (2020)

Mathematica Bohemica

In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point p in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various Pre T 2 , T i , i = 0 , 1 , 2 , 3 , structures at a point p are investigated. Finally, we examine the relationships between the generalized separation...

Taylor towers for Γ -modules

Birgit Richter (2001)

Annales de l’institut Fourier

We consider Taylor approximation for functors from the small category of finite pointed sets Γ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.

Taylor towers of symmetric and exterior powers

Brenda Johnson, Randy McCarthy (2008)

Fundamenta Mathematicae

We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, D k S p ⁿ and D k Λ ⁿ , in terms of the first terms in the Taylor towers of S p t and Λ t for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of S p t and Λ t . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for D k S p ⁿ and D k Λ ⁿ .

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