The articles [18], [5], [20], [11], [1], [16], [2], [21], [4], [3], [12], [17], [7], [8], [9], [10], [13], [14], [15], [6], and [19] provide the terminology and notation for this paper. In this paper j, k, n are natural numbers and C is a subset of E T satisfying conditions of simple closed curve. Let us consider C. The functor ApproxIndexC yielding a natural number is defined by: (Def. 1) Appr...

Let k be a field of characteristic p. We construct a new inflation functor for cohomological Mackey functors for finite groups over k. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor S 1 , when p is odd and G is an elementary abelian p-group. AMS Subject Classification : 18A25, 18G10, 18G15, 20J05.

We study the functor `2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its ...

We study a connection between mapping spaces of bimodules and infinitesimal over an operad. As main application motivation our work, we produce explicit delooping the manifold calculus tower associated to space smooth maps D m → n $D^m\rightarrow D^n$ discs, ⩾ $n\geqslant m$ , avoiding any given multisingularity coinciding with standard inclusion near boundary ∂ $\partial D^m$ . In particular, ...

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, have been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to loca...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

In this paper, we consider the forgetful functor from the category LDcpo of local dcpos (respectively, Dcpo of dcpos) to the category Pos of posets (respectively, LDcpo of local dcpos), and study the existence of its left and right adjoints. Moreover, we give the concrete forms of free and cofree S-ldcpos over a local dcpo, where S is a local dcpo monoid. The main results are: (1) The forgetful...