Manuscript Psy02-B@2 · Psy02-B-v2.tex · theorem · cfd06e2e

Theorem: Descent through reconstruction

Track B reconstruction, contacts, and supported references › An explicit presentation model · lines 2095–2115 · proof included or linked

Psy02-B@2#thm:descent

Back to manuscript

A linear candidate

F : P_{int} \to D^{'} (W)

factors uniquely through $Rec$ if and only if

ker Rec \subseteq ker F .

If $F$ is continuous, the induced map is continuous for the quotient topology.

Proof. A factoring map kills the kernel. Equal reconstructions differ by a kernel element, so the condition makes the induced value well defined. Surjectivity onto the range gives uniqueness. The quotient topology gives continuity.

Displayed formulas in this passage

unlabeled · line 2098
$F : P_{int} \to D^{'} (W)$
unlabeled · line 2102
$ker Rec \subseteq ker F .$

Nearby in this section

section: An explicit presentation model
section: An explicit presentation model