Homotopy cofibres, higher coassociativity and homotopy coalgebras

Lie Coalgebras and Rational Homotopy Theory, I: Graph Coalgebras

Homotopy Theory of Coalgebras over Operads

This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are deriv...

Homotopy Variation Map and Higher Homotopy Groups of Pencils

We prove in a synthetic manner a general Zariski-van Kampen type theorem for higher homotopy groups of pencils on singular complex spaces.

Higher Homotopy Operations

We provide a general definition of higher homotopy operations, encompassing most known cases, including higher Massey and Whitehead products, and long Toda brackets. These operations are defined in terms of the W -construction of Boardman and Vogt, applied to the appropriate diagram category; we also show how some classical families of polyhedra (including simplices, cubes, associahedra, and pe...

Vertex Coalgebras, Comodules, Cocommutativity and Coassociativity

We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, D∗, which hold on vertex coalgebras. The former two properties require grading. We then discuss comodule structure. We conclude by discussing instances where graded vertex coalgebras appear, particularly a...