covariant family of homomorphisms between Oriented structures.

Property Let h be an instance of HomOriented, then for all a, b and h in h a b holds:

1. start . amap h .=. pmap h . start.
2. end . amap h .=. pmap h . end.

Note The above property is equivalent to amap h . orientation .=. orientation . omap h.

disjunctive family of homomorphism between Oriented structures.

Properties Let HomOrientedDisjunctive h, then for all x, y and h in h x y holds:

1. If variant2 h == Covariant then holds:

   1. start . amap h .=. pmap h . start.
   2. end . amap h .=. pmap h . end.

2. If variant2 h == Contravariant then holds:

   1. start . amap h .=. pmap h . end.
   2. end ',' amap h .=. pmap h . start.

Note The above property is equivalent to orientation . amap h .=. omapDisj h . orientation.

induced application respecting the variant by applying opposite for Contravariant cases.

functorial morphismsm, i.e. Functorial and FunctorialPoint.

Note It's not mandatory being an homomorphism!

duality according to o on Oriented structures.

Properties Let DualisableOriented o s, then for all x and s in Struct s x holds:

1. start . toDualArw q s .=. toDualPnt q s . end.
2. end . toDualArw q s .=. toDualPnt q s . start.

where q is any proxy for o.

Note The above property is equivalent to orientation . toDualArw q s .=. toDualOrt q s . orientation.

the dual arrow given by DualisableOriented s o and induced by 'DualisableG s (->) o Id.

the dual point given by DualisableOriented s o and induced by DualisableG s (->) o Pnt.

the induced dual orientation.

the canonical Contravariant isomorphism on Oriented structures between x and Op x.