Duty / Obligation (typed Reg_C-edge)
A duty, in the τ-framework, is a typed obligation-edge in the Commitment Register: a τ-categorical morphism in Reg_C, sourced from an agent and indexed by register and domain (VII.L11), whose categorical-imperative closure (Kant-τ correspondence VII.D73) makes it universalizable. Cross-type comparison of duties is structurally ill-formed; apparent conflicts dissolve under correct typing.
τ-Definition
A duty, in the τ-framework, is a typed obligation-edge in the Commitment Register: a τ-categorical morphism in Reg_C, sourced from an agent and indexed by register and domain (VII.L11), whose categorical-imperative closure (Kant-τ correspondence VII.D73) makes it universalizable. Cross-type comparison of duties is structurally ill-formed; apparent conflicts dissolve under correct typing.
Categorical invariant. Δ̂ = a Reg_C-morphism d : σ → a typed by (register R ∈ {E,P,D,C}, domain k) such that d ∈ Fix(U_CI) (CI-closure); equivalently, a duty is a typed Reg_C-edge whose universalizability test under VII.D73 returns identity.
Primary registry anchor:
VII.D73
τ-Derivation Chain
-
I.K0— Universe Postulate -
VII.D04— Commitment Register Reg_C with codomain Stance -
VII.D72— Commitment Register Admissibility -
VII.L11— Duty Typing Lemma — duties are typed by register and domain -
VII.D67— Fairness Protocol — CI-test that duty must pass -
VII.D73— Kant-τ Correspondence — categorical imperative as the closure operator on duty
Phenomenological Correlate
A duty is instantiated whenever a typed Reg_C-edge sources an obligation that survives universalizability. Examples: Kantian perfect duties (don't lie); imperfect duties (cultivate talents); professional duties (fiduciary, medical, journalistic); role-relative duties; the famous 'duty conflicts' that dissolve once VII.L11 typing is applied.
Examples:
- Kantian perfect duties (don't lie, don't murder) — CI-closed sections of Reg_C^earned
- Kantian imperfect duties (cultivate talents, beneficence) — CI-closed but distributed across opportunities
- Fiduciary duty (trustee, board member, investment advisor) — typed by professional-role register
- Medical duty of care — typed by clinical-domain register, sourced from licensed agents
- Journalistic duty to truth — typed by epistemic-role register
- Apparent conflicts (Sophie's Choice; trolley problem) — dissolve or reduce under VII.L11 typing
- Filial duty in cross-cultural ethics — different domain-typings yield different valid edges
Register codomain: Stance (Reg_C — a duty is a typed CI-closed morphism of Reg_C; lives in Reg_C^earned for the agent who sources it; dual to the right that receives it)
Manuscript reference: manuscript-sources/book-07/part07/ch91.tex
Lean Coverage
Status: Skeleton
Module: TauLib.BookVII.Ethics.CIProof
Lean kind: theorem
Lean symbol: Tau.BookVII.Ethics.CIProof.duty_typing