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FALSE: every conservative right adjoint is monadic
Statement
False claim: every conservative right adjoint is monadic.
Facts & Assumptions
Given: The underlying-set functor from torsion-free abelian groups.
Torsion-free abelian groups give a conservative right adjoint that is not monadic (Torsion-free abelian groups give a conservative right adjoint that is not monadic).
A conservative functor reflects isomorphisms (Conservative functor).
Refutation
Apply the false implication to the underlying-set functor from [L1].
The functor has a left adjoint and reflects isomorphisms, so it is a conservative right adjoint and satisfies the antecedent by [L1] and [L2].
Its comparison misses abelian groups with nonzero torsion, so [L1] says it is not monadic. The antecedent is true and the conclusion false for this functor, refuting the claim.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
12 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- D. Mehrle, Category Theory Part III, Example 5.20(d) (standard reference, not scraped)