In this paper we give a new foundational, categorical formulation for operations and
relations and objects parameterizing them. This generalizes and unifies the theory of …

Many homotopy-coherent algebraic structures can be described by Segal-type limit
conditions determined by an “algebraic pattern”, by which we mean an∞-category equipped …

In this paper, we construct groupoid coloured operads governing props and wheeled props,
and show they are Koszul. This is accomplished by new biased definitions for (wheeled) …

Koszul duality is an important ingredient in the theory of algebraic operads. The classical
Koszul duality theory for associative algebras goes a long way back to Priddy [23], but a …

PROPs and their variants are extremely general and powerful machines that encode
operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as …

We develop further the theory of operads and analytic functors. In particular, we introduce
the bicategory $\operatorname {OpdBim} _ {\mathcal {V}} $ of operad bimodules, that has …

Operads are a powerful foundation for handling composition and substitution of various
structures. While at first the underlying combinatorics of operads concerned how trees are …

We study the category of algebras of substitudes (also known to be equivalent to the regular
patterns of Getzler and operads coloured by a category) equipped with a (semi) model …

A moment category is endowed with a distinguished set of split idempotents, called
moments, which can be transported along morphisms. Equivalently, a moment category is a …

We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-
category of substitudes of Day and Street (2003), and that the Feynman categories of …