Related papers: A prop structure on partitions

We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…

The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We first consider a function space of props to define the…

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

It is a classical result that the category of finitely-generated free monoids serves as a PROP for commutative bialgebras. Attaching permutations to fix the order of multiplication, we construct an extension of this category that is…

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of…

A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by…

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 study configuration spaces of framed points on oriented closed smooth manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of…

We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…

We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…

Long before the invention of Feynman diagrams, engineers were using similar diagrams to reason about electrical circuits and more general networks containing mechanical, hydraulic, thermodynamic and chemical components. We can formalize…

We introduce a new algebraic construction, {\em monop}, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of…

We construct for every $\infty$-operad $\mathcal{O}^\otimes$ with certain finite limits new $\infty$-operads of spectrum objects and of commutative group objects in $\mathcal{O}$. We show that these are the universal stable resp. additive…

These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…

We explore a natural extension of braid arrangements in the context of determinantal arrangements. We show that these determinantal arrangements are free divisors. Additionally, we prove that free determinantal arrangements defined by the…

Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamiltonian mechanics and gradient descent depend crucially on a…

We calculate mod-p cohomology of extended powers, and their group completions which are free infinite loop spaces. We consider the cohomology of all extended powers of a space together and identify a Hopf ring structure with divided powers…

Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…

Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible composition factors and deduce consequences…