@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));
}
@Test
public void testCanonicalExponentialIso() {
DOT dot1 = fixtures.dotFoo();
DOT dot2 = fixtures.dotBar();
ExponentialDiagram<DOT, ARROW> expA = _topos.getExponentialDiagram(dot1, dot2);
ExponentialDiagram<DOT, ARROW> expB = _topos.getExponentialDiagram(dot1, dot2);
ARROW isoAB = _topos.canonicalIso(expA, expB);
ARROW isoBA = _topos.canonicalIso(expB, expA);
DOT dotA = exponentialDot(expA);
DOT dotB = exponentialDot(expB);
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));
}
