2 problems

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The locally finite satellite conjecture for singular homology and homotopy
Locally finite satellite conjecture. The left satellites are naturally isomorphic to singular homology:
Conjectureopencosheaf-homology homotopy-theory topologyarXiv posted 2 days ago
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The pro-homology conjecture for cosheaf homology satellites
Pro-homology conjecture. On the standard site $OPEN(X)$ , if $X$ is Hausdorff paracompact, then
Conjectureopencosheaf-homology shape-theory topologyarXiv posted 2 days ago

The locally finite satellite conjecture for singular homology and homotopy