Revert "Remove obsolete type checks"

This reverts commit b6ef396.

Jeroen noted:

Sorry, I was wrong. At least some of the type checks are still needed,
because equal parents does not imply equal types here. For example:
```
 sage: R.<x,y> = PolynomialRing(QQ, 2)
 sage: S.<a,b> = R.quo(x^2 + y^2)
 sage: phi = S.cover()
 sage: alpha = R.hom(R, (0,0))
 sage: psi = phi.pre_compose(alpha)
 sage: parent(psi) is parent(phi)
 True
 sage: type(psi) is type(phi)
 True
```

src/sage/rings/morphism.pyx

@@ -524,6 +524,9 @@ cdef class RingMap_lift(RingMap):
         if op not in [Py_EQ, Py_NE]:
             return NotImplemented
 
+        if not isinstance(other, RingMap_lift):
+            return (op == Py_NE)
+
         # Since they are lifting maps they are determined by their
         # parents, i.e., by the domain and codomain, since we just
         # compare those.
@@ -959,6 +962,9 @@ cdef class RingHomomorphism_coercion(RingHomomorphism):
         if op not in [Py_EQ, Py_NE]:
             return NotImplemented
 
+        if not isinstance(other, RingHomomorphism_coercion):
+            return (op == Py_NE)
+
         # Since they are coercion morphisms they are determined by
         # their parents, i.e., by the domain and codomain, so we just
         # compare those.
@@ -1171,6 +1177,11 @@ cdef class RingHomomorphism_im_gens(RingHomomorphism):
             sage: loads(dumps(f2)) == f2
             True
         """
+        if not isinstance(other, RingHomomorphism_im_gens):
+            if op in [Py_EQ, Py_NE]:
+                return (op == Py_NE)
+            return NotImplemented
+
         return richcmp(self.__im_gens, (<RingHomomorphism_im_gens>other).__im_gens, op)
 
     def __hash__(self):
@@ -1460,6 +1471,10 @@ cdef class RingHomomorphism_from_base(RingHomomorphism):
             sage: f1M == loads(dumps(f1M))
             True
         """
+        if not isinstance(other, RingHomomorphism_from_base):
+            if op in [Py_EQ, Py_NE]:
+                return (op == Py_NE)
+            return NotImplemented
         return richcmp(self.__underlying, (<RingHomomorphism_from_base>other).__underlying, op)
 
     def _repr_defn(self):
@@ -1635,6 +1650,9 @@ cdef class RingHomomorphism_cover(RingHomomorphism):
         if op not in [Py_EQ, Py_NE]:
             return NotImplemented
 
+        if not isinstance(other, RingHomomorphism_cover):
+            return (op == Py_NE)
+
         return richcmp(self.parent(), other.parent(), op)
 
     def __hash__(self):
@@ -1831,6 +1849,9 @@ cdef class RingHomomorphism_from_quotient(RingHomomorphism):
         if op not in [Py_EQ, Py_NE]:
             return NotImplemented
 
+        if not isinstance(other, RingHomomorphism_from_quotient):
+            return (op == Py_NE)
+
         cdef RingHomomorphism_from_quotient left = self
         cdef RingHomomorphism_from_quotient right = other
         return richcmp(left.phi, right.phi, op)