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To describe homotopy invariant algebraic structures on spaces, there are different approaches. The Stasheff / Boardman–Vogt / May approach, where operations and equations are replaced by spaces of ...

Let $\varphi:A\to \mathrm{Ass}$ be an $A_\infty$-operad in topological spaces, and let $X$ be an $A$-algebra. I see three possibilities to construct a delooping out of $X$: Rectify $X$ by taking the ...

Informally, an $A_\infty$-space is a monoid whose laws are only satisfied up to homotopy. Let’s define now what I will call a "homotopic monoid" to be a space $M$ together with a point $e\in{}M$ and ...

Suppose we are given a fixed ambient symmetric monoidal model category (I'm mostly interested in chain complexes over char zero fields). Then we have the notion of an $E_n$-operad in that category. ...