Related papers: Parametrized higher category theory and higher alg…
This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous…
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
The notion of (symmetric) coloured operad or "multicategory" can be obtained from the notion of commutative algebra through a certain general process which we call "theorization" (where our term comes from an analogy with William Lawvere's…
We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
Boundaries, GNH, and parametrized theories. It takes three to tango. This is the motto of my doctoral thesis and the common thread of it. The thesis is structured as follows: after some acknowledgments and a brief introduction, chapter one…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
We present generalized algebraic theories corresponding to slightly modified versions of two of the type theories in our paper Type Theory with Explicit Universe Polymorphism. We first present a generalized algebraic theory for categories…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the…
We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…
These are extended notes for a series of lectures on Hall algebras given at the CRM Barcelona in February 2015. The basic idea of the theory of Hall algebras is that the collection of flags in an exact category encodes an associative…
We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of 1-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a…
In this survey we discuss some combinatorial aspects of higher cluster categories.
The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed…