Homotopy-coherent algebra via Segal conditions

Operator space structure on Feichtinger’s Segal algebra

We extend the definition, from the class of abelian groups to a general locally compact group G, of Feichtinger’s remarkable Segal algebra S0(G). In order to obtain functorial properties for non-abelian groups, in particular a tensor product formula, we endow S0(G) with an operator space structure. With this structure S0(G) is simultaneously an operator Segal algebra of the Fourier algebra A(G)...

Homotopy Coherent Category Theory

Homotopy Coherent Structures

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to catalog the higher homotopical information required to restore constructibility (or more precisely, functoriality) in such “up to homotopy” settings. The firs...

Algebra + Homotopy = Operad

This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in Algebra, Geometry, Topology, and Mathematical Physics. (This text is acc...

Towards an Homotopy Theory of Process Algebra

This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra ...