// Given two arrows with the same source, check we can multiply them
// and get an arrow to the product of their targets
@Test
public void testProductOf2() {
ARROW p = fixtures.arrowFooToBar();
ARROW q = fixtures.arrowFooToBaz();
DOT a = p.getSource();
DOT b = p.getTarget();
DOT c = q.getTarget();
assertTrue(a == q.getSource());
ProductDiagram<DOT, ARROW> diagram = _topos.product(b, c);
List<ARROW> arrowComponents = new ArrayList<ARROW>();
arrowComponents.add(p);
arrowComponents.add(q);
ARROW pxq = diagram.multiplyArrows(a, arrowComponents);
List<ARROW> projections = diagram.getProjections();
assertTrue(p.equals(projections.get(0).compose(pxq)));
assertTrue(q.equals(projections.get(1).compose(pxq)));
}
@Test
public void testCanonicalProductIso() {
DOT dot1 = fixtures.dotBar();
DOT dot2 = fixtures.dotFoo();
ProductDiagram<DOT, ARROW> productA = _topos.product(dot1, dot2);
ProductDiagram<DOT, ARROW> productB = _topos.product(dot1, dot2);
ARROW isoAB = _topos.canonicalIso(productA, productB);
ARROW isoBA = _topos.canonicalIso(productB, productA);
DOT dotA = productA.getProduct();
DOT dotB = productB.getProduct();
assertSame(isoAB.getSource(), dotA);
assertSame(isoAB.getTarget(), dotB);
assertSame(isoBA.getSource(), dotB);
assertSame(isoBA.getTarget(), dotA);
assertEquals(dotA.getIdentity(), isoBA.compose(isoAB));
assertEquals(dotB.getIdentity(), isoAB.compose(isoBA));
}