The primary goal of this article is to set up a general theory of coherent cellular
approximations of the diagonal for families of polytopes by developing the method …

Massey Products for Graph Homology Page 1 BC Ward (2022) “Massey Products for Graph
Homology,” International Mathematics Research Notices, Vol. 2022, No. 11, pp. 8086–8161 …

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 …

Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0 $,
these higher categorical structures are modelled by differential graded Lie algebras, but in …

For a Koszul operad 𝒫 P, there are several existing approaches to the notion of a homotopy
between homotopy morphisms of homotopy 𝒫 P-algebras. Some of those approaches are …

Curved algebras are a generalization of differential graded algebras which have found
numerous applications recently. The goal of this foundational article is to introduce the …

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A theorem of Pridham and Lurie provides an equivalence between formal moduli problems
and Lie algebras in characteristic zero. We prove a generalization of this correspondence …

The aim of this note is to give a detailed account of how symmetric operads can be
constructed from planar (non-symmetric) operads, and to carefully spell out the algebraic …

We present a Markl-style definition of operads colored by a small category. In the presence
of a unit these are equivalent to substitudes of Day and Street. We show that operads …