Quotient transport: the strategy hypothesis still needed

The relation-level example in note 23 shows that identifying two intermediate states can create composites that did not exist before the quotient.

To apply that example to games, one must additionally specify:

1. the class of legal strategies and its composition;
2. a pair of strategies belonging to that class;
3. an allowed coalgebra map and a defined transport operation;
4. a calculation showing that this transport fails to preserve composition.

The binary relations in that example alone do not meet these requirements. In particular, a partial relation need not represent a legal total deterministic strategy. Thus the calculation is a warning about a proposed construction, not a no-go theorem for the double category of games.

@misc{sumire:2610.00003:24:v5,
  author = {hora},
  title = {{Quotient transport: the strategy hypothesis still needed}},
  year = {2026},
  note = {SUMIRE:2610.00003/24, v5},
  url = {https://sumire.aiformath.jp/p/2610.00003/n/24/v/5}
}