Related papers: Higher-order CPM Constructions
This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, and therefore a sequence of four successively stricter…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
This paper introduces and studies a categorical analogue of the familiar monoid semiring construction. By introducing an axiomatisation of summation that unifies notions of summation from algebraic program semantics with various notions of…
We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing "invariant versions" of iterated integrals of modular forms. The construction will be based on an extension of…
We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We study two kinds of generalizations of symmetric block designs to higher dimensions, the so-called $\mathcal{C}$-cubes and $\mathcal{P}$-cubes. For small parameters, all examples up to equivalence are determined by computer calculations.…
We study monoidal categorifications of certain monoidal subcategories $\mathcal{C}_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional…
We use categorification of monoid actions to study algebraic geometry over symmetric monoidal categories. This brings together the relative algebraic geometry over symmetric monoidal categories developed by To\"{e}n and Vaqui\'{e}, along…
We extend the modular orbits method of constructing a two-dimensional orbifold conformal field theory to higher genus Riemann surfaces. We find that partition functions on surfaces of arbitrary genus can be constructed by a straightforward…
We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…
We provide a construction for holes into which morphisms of abstract symmetric monoidal categories can be inserted, termed the polyslot construction pslot[C], and identify a sub-class srep[C] of polyslots that are single-party…
The filtered derived category of an abelian category has played a useful role in subjects including geometric representation theory, mixed Hodge modules, and the theory of motives. We develop a natural generalization using current methods…
We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing…
Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…
We define a bar construction endofunctor on the category of commutative augmented monoids $A$ of a symmetric monoidal category $\mathcal{V}$ endowed with a left adjoint monoidal functor $F:s\mathbf{Set}\to \mathcal{V}$. To do this, we need…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
Baez-Dolan type plus constructions serve three main purposes: They (1) corepresent categorical bimodules that are monoids with respect to a plethysm product, (2) allow to define functors as bimodule monoids, and thereby algebras over…
Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…