in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

We give a new characterization of smashing subcategories in a compactly generated triangulated category and prove a modiied version of Ravenel's telescope conjecture in this setting. Our results apply in particular to the stable homotopy category. Our approach, however, is purely algebraic; it is based on an analysis of pure injective objects in a compactly generated triangulated category.

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective s...

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology a...