If (π, V ) is an admissible representation of a p-adic reductive group G and P = MN is a parabolic subgroupwith unipotent radicalN , its Jacquet module VN is the universalN -trivial quotientH0(N,V ) of V by the span of vectors π(n)v − v (n ∈ N ). One fundamental property is that V VN is an exact functor. This construction plays an important role in homomorphisms into representations induced fro...

In this article we study the digital homology groups of digital images which are based on the singular homology groups of topological spaces in algebraic topology. Specifically, we define a digitally standard n-simplex, a digitally singular nsimplex, and the digital homology groups of digital images with k -adjacency relations. We then construct a covariant functor from a category of digital im...

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

Inspired by Lambek's work on categorial grammar, we examine the proposal that the theory of biclosed monoidal categories can serve as a foundation for a formal theory of natural language. The emphasis throughout is on the derivation of the axioms for these categories from linguistic intuitions. When Montague's principle that there is a homomorphism between syntax and semantics is reened to the ...

Consider a connected topological space $$X$$ with point $$x$$ in and let $$K$$ be field the discrete topology. We study Tannakian category of finite-dimensional (flat) vector bundles on its dual $$\pi(X,x)$$ respect to fiber functor . The maximal pro-étale quotient is étale fundamental group studied by Kucharczyk Scholze. For well-behaved spaces, pro-algebraic completion ordinary group. obtain ...

Abstract We show how to functorially attach continuous $p$-adic representations of the profinite fundamental group vector bundles with numerically flat reduction on a proper rigid analytic variety over ${{\mathbb {C}}}_p$. This generalizes results by Deninger and Werner for smooth algebraic varieties. Our approach uses pro-étale site introduced Scholze. enables us get rid smoothness condition w...

In this article we define the tensor product of partial acts over a semigroup and prove several properties product. We also notion polite biact, which is needed to actions on acts. Finally, that certain functor left adjoint hom-functor

We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an involutive “duality” functor from the bounded derived category of modules over the distribution algebra of G with coadmissible cohomology to itself. on the subcateg...

For a functor F ⊃ Id on the category of metrizable compacta, we introduce a conception of a linear functorial operator T = {TX : Pc(X) → Pc(FX)} extending (for each X) pseudometrics from X onto FX ⊃ X (briefly LFOEP for F ). The main result states that the functor SP G of G-symmetric power admits a LFOEP if and only if the action of G on {1, . . . , n} has a one-point orbit. Since both the hype...

We define an “algebraic” version of the Goodwillie tower, P alg n F (X), that depends only on the behavior of F on coproducts of X . When F is a functor to connected spaces or grouplike H-spaces, the functor P alg n F is the base of a fibration |⊥ F | → F → P alg n F, whose fiber is the simplicial space associated to a cotriple ⊥ built from the (n + 1) cross effect of the functor F . When the c...