نتایج جستجو برای: enriched category
تعداد نتایج: 141231 فیلتر نتایج به سال:
In a paper of 1974, Brian Day employed a notion of factorization system in the context of enriched category theory, replacing the usual diagonal lifting property with a corresponding criterion phrased in terms of hom-objects. We set forth the basic theory of such enriched factorization systems. In particular, we establish stability properties for enriched prefactorization systems, we examine th...
Let R be a (unital) commutative ring, andG be a finite group with order invertible in R. We introduce new idempotents εT,S in the double Burnside algebra RB(G,G) of G over R, indexed by conjugacy classes of minimal sections (T, S) of G (i.e. sections such that S ≤ Φ(T )). These idempotents are orthogonal, and their sum is equal to the identity. It follows that for any biset functor F over R, th...
We present a weak form of a recognition principle for Quillen model categories due to J.H. Smith. We use it to put a model category structure on the category of small categories enriched over a suitable monoidal simplicial model category. The proof uses a part of the model structure on small simplicial categories due to J. Bergner. We give an application of the weak form of Smith’s result to le...
In [6] Higson showed that the formal properties of the Kasparov KK -theory groups are best understood if one regards KK (A, B) for separable C∗-algebras A, B as the morphism set of a category KK . In category language the composition and exterior KK product give KK the structure of a symmetric monoidal category which is enriched over abelian groups. We show that the enrichment of KK can be lift...
2 Categories and examples 7 2.1 The definition of a category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Categories as graphs with composition . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Categories as partial semigroups . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Categories as enriched categories . . . . . . . . . . . . . . . . . . . . . . . . ....
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory. Motivated by some key results of the 1970s, the paper develops all needed ingredients from the theory of quantaloids in order to place essential results of categori...
We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key element of our construction is a spectrally-enriched functor from a spectrally-enriched version of permutative categories to the category of spectra that is ...
This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P , the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak -lattices and -...
Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to G. M. Kelly in the 1960s that there is a very close connection between these phenomena. In this first part of a two-part series on this subject, we show that the assignment to each symmetric monoidal closed category V its associat...
1.3. De nition. ABSTRACT. We apply enriched category theory to study Cauchy completeness in continuity spaces. Our main result is the equivalence in continuity spaces of the category theoretic and the uniform notions of Cauchy completeness. This theorem, which generalizes a result of Lawvere for quasi-metric spaces, makes a natural connection between the category-theoretic and topological aspec...
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