// Given a monic and an arrow to premultiply it, check we can factorize this out again via the
// subobject classifier and its induced pullback
@Test
public void testSubobjectClassifier() {
ARROW monicPrefix = fixtures.arrowBubToFoo();
ARROW monic = fixtures.arrowMonicFooToBar();
SubobjectClassifier<DOT, ARROW> classifier = _topos.getSubobjectClassifier();
ARROW truth = classifier.getTruth();
TerminatorDiagram<DOT, ARROW> tDgm = _topos.getTerminatorDiagram();
DOT terminator = tDgm.getTerminator();
assertTrue(terminator == truth.getSource());
assertTrue(monicPrefix.getTarget() == monic.getSource());
PullbackDiagram<DOT, ARROW> pullback = classifier.pullbackMonic(monic);
// Verify that this really is a pullback diagram and can factor out the monic.
ARROW north = pullback.getNorth();
ARROW south = pullback.getSouth();
ARROW west = pullback.getWest();
ARROW east = pullback.getEast();
assertTrue(north.getSource() == west.getSource());
assertTrue(north.getTarget() == east.getSource());
assertTrue(south.getSource() == west.getTarget());
assertTrue(south.getTarget() == east.getTarget());
assertTrue(east.compose(north).equals(south.compose(west)));
// it's a commutative square: now, are the right bits in place?
assertTrue(south == truth); // seems reasonable to insist on strict equality here
assertTrue(north == monic);
// pull back the composition...
ARROW composition = monic.compose(monicPrefix);
ARROW constant = tDgm.getConstantArrow(composition.getSource());
// sanity check: just make sure it can be pulled back...
assertTrue(east.compose(composition).equals(south.compose(constant)));
List<ARROW> commutingArrows = new ArrayList<ARROW>();
commutingArrows.add(composition);
commutingArrows.add(constant);
ARROW factor =
pullback.factorize(commutingArrows); // should have extract the original prefix arrow
assertTrue(monicPrefix.equals(factor));
}
