Functorial CW-approximation
Philip S. Hirschhorn
TL;DR
This paper presents a new functorial CW-approximation construction that is strictly functorial, unlike the traditional homotopy-based approach, and it preserves inclusions and intersections of subspaces.
Contribution
It introduces a functorial CW-approximation method that strictly respects inclusions and intersections, improving upon the non-functorial classical construction.
Findings
Constructs a functorial CW-approximation that is strictly functorial.
Preserves inclusions of subspaces as inclusions of subcomplexes.
Commutes with intersections of subspaces.
Abstract
The usual construction of a CW-approximation is functorial up to homotopy, but it is not functorial. In this note, we construct a functorial CW-approximation. Our construction takes inclusions of subspaces into inclusions of subcomplexes, and commutes with intersections of subspaces of a fixed space.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra