We review Quillen's concept of a model category as the proper setting for deening derived functors in non-abelian settings, explain how one can transport a model structure from one category to another by mean of adjoint functors (under suitable assumptions), and deene such structures for categories of cosimplicial coalgebras. 1. Introduction Model… (More)
We define a sequence of purely algebraic invariants – namely, classes in the Quillen cohomology of the Π-algebra π * X – for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract Π-algebra can be realized as the homotopy Π-algebra of a space.
Given a diagram of …–algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized …–algebras. This extends a program begun by… (More)
We describe an obstruction theory for a given topological space X to be an H-space, in terms of higher homotopy operations, and show how this theory can be used to calculate such operations in certain cases.
We show how a certain type of CW simplicial resolutions of spaces by wedges of spheres may be constructed, and how such resolutions yield an obstruction theory for a given space to be a loop space.
Given a suitable functor T : C → D between model categories, we define a long exact sequence relating the homotopy groups of any X ∈ C with those of T X, and use this to describe an obstruction theory for lifting an object G ∈ D to C. Examples include finding spaces with given homology or homotopy groups. A number of fundamental problems in algebraic… (More)
We present a simple model to estimate the subsidy cost embedded in a global feed-in tariff (GFIT) to simultaneously stimulate electrification and the take-up of renewable energy sources for electricity generation in developing countries. The GFIT would subsidize developing countries for investments they make in generation capacity for renewable electricity… (More)
We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.