On the idempotency of some composite functors
Ramon Flores
TL;DR
This paper provides examples showing that the composition of certain localization and cellularization functors in the category of spaces may not be idempotent, challenging assumptions about their behavior.
Contribution
It introduces specific examples demonstrating non-idempotency of composed localization and cellularization functors in topological spaces.
Findings
Composition of some localization and cellularization functors is not idempotent.
Counterexamples to idempotency in the category of spaces.
Highlights limitations of functor compositions in homotopy theory.
Abstract
In this note we present examples of localization functors (in the category of spaces) whose composition with certain cellularization functors is not idempotent, and vice versa.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models