nLab trace-class map

Contents

Context

(,1)(\infty,1)-Category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

 Definition

Given a closed monoidal ( , 1 ) (\infty, 1) -category 𝒞\mathcal{C}, with unit I𝒞I \in \mathcal{C}, tensor product ()():𝒞×𝒞𝒞(-)\otimes (-):\mathcal{C} \times \mathcal{C} \to \mathcal{C}, and internal hom [(),()]:𝒞×𝒞𝒞[(-), (-)]:\mathcal{C} \times \mathcal{C} \to \mathcal{C}, let a𝒞a \in \mathcal{C} and b𝒞b \in \mathcal{C} be objects in 𝒞\mathcal{C}. Let f:abf:a \to b be a map. ff is a trace-class map or nuclear map if ff lies in the image of the natural map Hom(I,[a,I]b)Hom(a,b)\mathrm{Hom}(I, [a, I] \otimes b) \to \mathrm{Hom}(a, b).

See also

References

Created on May 26, 2022 at 13:55:47. See the history of this page for a list of all contributions to it.