Related papers: A guide to tensor-triangular classification
We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.
Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the classification theorem of thick subcategories of the…
We construct a left semi-model structure on the category of intensional type theories (precisely, on $\mathrm{CxlCat_{Id,1,\Sigma(,\Pi_{ext})}}$). This presents an $\infty$-category of such type theories; we show moreover that there is an…
This is a survey article to appear in the "Handbook on Teichmueller Theory".
Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines,…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central…
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We…
Closed formulas for the multilinear rank of trifocal Grassmann tensors are obtained. An alternative process to the standard HOSVD is introduced for the computation of the core of trifocal Grassmann tensors. Both of these results are…
These notes give a brief introduction to the category of spectra as defined in stable homotopy theory. In particular, Section 5 discusses an extensive list of examples of spectra whose properties have been found to be interesting.
We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…
We introduce the notion of $\pi$-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories.…
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
For a given modular tensor category we study representations of the corresponding tube category whose isomorphism classes are modular invariant matrices. In particular, we provide a characterization of these representations in terms of the…
We describe $L_\infty$-algebras governing homotopy relative Rota-Baxter Lie algebras and triangular $L_\infty$-bialgebras, and establish a map between them. Our formulas are based on a functorial approach to Voronov's higher derived…
The extriangulated category is a simultaneous generalization of exact categories and triangulated categories. H. Nakaoka and Y. Palu have proved that the homotopy category of an admissible model structure on a weakly idempotent complete…
By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category $\T$ is equivalent to the topological structure of its Balmer spectrum $\spc \T$. Motivated by this theorem, we discuss…
The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…
This dissertation contains a comprehensive study of the topology of 2-manifolds and a complementary analysis of the work done by Edwin E. Moise, L. V. Ahlfors and Ian Richards. Our aim is to study the well known classification of surfaces.…