To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

We study categorial properties of the operadic twisting functor Tw. In particular, we show that
Tw is a comonad. Coalgebras of this comonad are operads for which a natural notion of …

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

We extend the Chern character on K-theory, in its generalization to the Chern-Dold
character on generalized cohomology theories, further to (twisted, differential) non-abelian …

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-
Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new …

We construct two algebraic versions of homotopy theory of rational disconnected topological
spaces, one based on differential graded commutative associative algebras and the other …

This online-only material supplements the article “Euler characteristics for spaces of string
links and the modular envelope of L∞,” published in Homology, Homotopy and …

We recover some recent results by Dotsenko, Shadrin, and Vallette on the Deligne groupoid
of a pre-Lie algebra, showing that they follow naturally by a pre-Lie variant of the PBW …

We describe $ L_\infty $-algebras governing triangular $ L_\infty $-bialgebras and homotopy
relative Rota-Baxter Lie algebras and establish a map between them. Our formulas are …

Using the theory of extensions of algebras, we construct rational homotopy models for
classifying spaces of fibrations, giving answers in terms of classical homological functors …