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The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
Interpolation categories for homology theories
For a homological functor from a triangulated category to an abelian category
satisfying some technical assumptions we construct a tower of interpolation
categories. These are categories over which the functor factorizes and which
capture more and more information according to the injective dimension of the
images of the functor. The categories are obtained by proving the existence of
truncated versions of resolution or -model structures. Examples of
functors fitting in our framework are given by every generalized homology
theory represented by a ring spectrum satisfying the Adams-Atiyah condition.
The constructions are closely related to the modified Adams spectral sequence
and give a very conceptual approach to the associated moduli problem and
obstruction theory. As application we establish an isomorphism between certain
E(n)-local Picard groups and some Ext-groups.Comment: 40 pages, corrected version of second part of the replaced version,
first part will appear sepparately as "Truncated resolution model
structures", to appear in JPA
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