White light can be decomposed into different colors, and a complex sound wave its partials. While the physics behind transverse longitudinal waves is quite several theories have been developed to investigate complexity of colors timbres, we try model their structural similarities through language categories. Then, consider color mixing transition in painting, comparing them with timbre superpos...

Abstract Smooth and proper dg-algebras have an Euler class valued in the Hochschild homology of algebra. This is worthy this name since it satisfies many familiar properties including compatibility with pairing on algebra that its opposite. Riemann–Roch theorems [21, 14]. In paper, we prove a broad generalization these theorems. We generalize from bicategory their bimodules to symmetric monoida...

We investigate the effect on Cauchy complete objects of the change of base 2-functor V-Cat → W-Cat induced by a two-sided enrichment V → W. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced in [Wal82] is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment F : V → W between lo...

As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into bicategories. Foldings are equivalent to connection pairs, and also to thin structures if the vertical and horizontal morphisms coincide. In a sense, the squares of a do...

Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are Morita equivalent if and only if they are isomorphic objects in the bicategory. We repeat this construction for von Neumann algebras. Von Neumann algebras f...

From the outset, the theories of ordinary categories and of additive categories were developed in parallel. Indeed additive category theory was dominant in the early days. By additivity for a category I mean that each set of morphisms between two objects (each “hom”) is equipped with the structure of abelian group and composition on either side, with any morphism, distributes over addition: tha...