For spaces homeomorphic to finite simplicial complexes, the assembly functor admits a fully faithful right adjoint, yielding a Whitehead category and torsion cosheaf that recover Whitehead torsion via K-theory.
Algebraic𝐾-theory of topological spaces. I
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Whitehead torsion and the kernel of assembly
For spaces homeomorphic to finite simplicial complexes, the assembly functor admits a fully faithful right adjoint, yielding a Whitehead category and torsion cosheaf that recover Whitehead torsion via K-theory.