Manuscript XXII-C@1 · XXII-C.tex · definition · b9a05a24

Definition: Component quotient

The frozen order-forming operation › Raw experiment-use relation · lines 589–612

XXII-C@1#def:quotient, XXII-C@1#eq:scc, XXII-C@1#eq:component-order

Define

p \sim_{D} q ⟺ p ⇝_{D} q and q ⇝_{D} p .

Let

E_{D} = E / \sim_{D}, [p] ⪯_{D} [q] ⟺ p ⇝_{D} q .

The represented objects are strongly connected components of experiment-use labels. They are not automatically the original individual operation events.

Displayed formulas in this passage

XXII-C@1#eq:scc · line 592
$p \sim_{D} q ⟺ p ⇝_{D} q and q ⇝_{D} p .$
XXII-C@1#eq:component-order · line 601
$E_{D} = E / \sim_{D}, [p] ⪯_{D} [q] ⟺ p ⇝_{D} q .$

Nearby in this section

section: Raw experiment-use relation
section: Raw experiment-use relation
theorem: Theorem: Order extraction
section: Raw experiment-use relation
lemma: Lemma: Why cycles cannot be represented injectively without a quotient
example: Example: A quotient is a substantive change of carrier