Minimal models for graph-related (hyper)operads

预层与算子代数态射的最小模型：基于盒算子Koszul对偶

A minimal model for prestacks and morphisms of operadic algebras via Koszul duality for box operads

本文通过盒算子的Koszul对偶理论，为编码$P$-代数态射和松弛预层的盒算子建立了最小模型，解决了Markl的开放问题。

Minimal fibrations of dendroidal sets

We prove the existence of minimal models for fibrations between dendroidal sets in the model structure for infinity-operads, as well as in the covariant model structure for algebras and in the stable one for connective spectra. In an appendix, we explain how our arguments can be used to extend the results of Cisinski, giving the existence of minimal fibrations in model categories of presheaves over generalised Reedy categories of a rather common type. Besides some applications to the theory of algebras over infinity-operads, we also prove a gluing result for parametrized connective spectra (or…

弯曲 operad 演算

Curved operadic calculus

本文建立弯曲 operad 的演算与同伦理论，提出弯曲绝对 operad、完备 Bar–Cobar 伴随及模型结构，并据此得到弯曲泛包络代数、最小余纤维分解与弯曲代数的同伦转移定理。

Koszul Feynman 范畴

Koszul Feynman Categories

本文证明了所有立方 Feynman 范畴都是 Koszul 的，并由此构造出显式极小的余纤维化解，为基于图和非基于图的广义 operad 提供 $\infty$ 版本模型。

Feynman Categories

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 operads and all their cousins including but not limited to PROPs, modular operads, twisted (modular) operads, properads, hyperoperads, their colored versions, as well as algebras over operads and an abundance of other related structures, such as crossed simplicial groups, the augmented simplicial category or FI--modules. The usefulness of this approach is that it allows us to handle all the classical as well as more esoteric …