Infinity-Operads DemystifiedPublished 5/6/2016. algtop higher-cat math operadsThe purpose of this post is to record the definition of ∞-operads and explain why it works like that. For this I'm using Lurie's definition of ∞-operads; there is also a definition by Cisinski--Moerdijk--Weiss using dendroidal sets, about which I…

The Milnor–Moore TheoremPublished 3/10/2016. algtop mathThis post is about the Milnor--Moore theorem, a powerful tool describing the structure of (co)commutative Hopf algebras. Like the Eckmann--Hilton argument , it shows that having multiple compatible operations on the same object can lead to…

Acyclic ModelsPublished 1/15/2016. algtop mathThe theorem(s) of acyclic models are a rather powerful technique for proving that some functors defined on truncated chain complexes can be extended in higher dimensions, and that two such functors are homotopic, by proving it on a small class of…

About Abelian BimodulesPublished 1/6/2016. algtop math operadsThis post is about something somewhat weird I noticed about infinitesimal bimodules over operads and their relationships with some operads. I don't know if it's something significant, and I'd definitely be interested to hear more about it. Context…

The Eckmann–Hilton ArgumentPublished 12/23/2015. algtop mathAs promised, this post is about the famous Eckmann--Hilton argument . This argument, on the surface, looks like a simple algebraic trick; but it has deep consequences, which I will now try to explain. This post is an expanded version of a math.SE…