Nuclear and trace ideals in tensored-categories

TL;DR: In this article, the notion of relative trace was introduced, motivated by an observation about the category of vector spaces and linear transformations and built upon the categorical trace of Joyal, Street, and Verity.

TL;DR: An enhanced version of the Radon-Nikodým theorem is derived that makes explicit the approximating functions, thereby allowing the coordinated construction of multiple simultaneous derivatives.

TL;DR: It is shown that distributional equivalence is equivalent to bisimilarity as well, using a characterization of distributional equivalent transition systems through ergodic morphisms.

TL;DR: The paper studies extensional reflexivity in compact closed categories and its relationship to Frobenius algebras. It characterizes extensionally reflexive objects, strictifies reflexivity, and demonstrates the presence of interesting algebraic structures in such objects.

TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.

TL;DR: In this paper, the convergence of distributions is considered in the context of conditional probability, i.e., random variables and expected values, and the probability of a given distribution converging to a certain value.

TL;DR: In this article, the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certain products using instruction manuals, which are clearlybuilt to give step-by-step information about how you ought to go ahead in operating certain equipments.