A Solution of Deligne's Hochschild Cohomology Conjecture

[hal-00773001, v1] Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

Second Hochschild Cohomology of Convolution Algebras

Higher categories, colimits, and the blob complex.

We summarize our axioms for higher categories, and describe the "blob complex." Fixing an n-category , the blob complex associates a chain complex B(*)(W;C) to any n-manifold W. The zeroth homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W = S(1)...

A Counterexample to a Conjecture of Barr

We discuss two versions of a conjecture attributed to M Barr The Harrison cohomology of a commutative algebra is known to coincide with the Andr e Quillen cohomology over a eld of characteristic zero but not in prime characteristics The conjecture is that a modi ed version of Harrison cohomology taking into account torsion always agrees with Andr e Quillen cohomology We give a counterexample De...