diff --git a/examples/Chapter2.ipynb b/examples/Chapter2.ipynb
index 0b576ba..51e1a1b 100644
--- a/examples/Chapter2.ipynb
+++ b/examples/Chapter2.ipynb
@@ -15,7 +15,7 @@
       "  Load 1 ASDF system:\n",
       "    kenzo\n",
       "; Loading \"kenzo\"\n",
-      "\n"
+      "..\n"
      ]
     },
     {
@@ -102,21 +102,22 @@
        "2. BCC, an object of type CHAIN-COMPLEX, the bottom chain complex C. Its reader\n",
        "   function is BCC1.\n",
        "\n",
-       "3. F, an object of type MORPHISM representing the morphism f. Its reader\n",
+       "3. F, an object of type MORPHISM representing the chain morphism f. Its reader\n",
        "   function is F1.\n",
        "\n",
-       "4. G, an object of type MORPHISM representing the morphism g. Its reader\n",
+       "4. G, an object of type MORPHISM representing the chain morphism g. Its reader\n",
        "   function is G1.\n",
        "\n",
-       "5. H, an object of type MORPHISM representing the morphism h. Its reader\n",
-       "   function is H1.\n",
+       "5. H, an object of type MORPHISM representing the morphism of graded modules h.\n",
+       "   Its reader function is H1.\n",
        "\n",
        "9. IDNM, an integer, a system-generated identifier for this object. Its reader\n",
        "   function is IDNM.\n",
        "\n",
-       "10. ORGN, a list containg a comment indicating the origin of the object. The\n",
-       "    should be unique (per session), since it is used in the implementation for\n",
-       "    caching purposes. Its reader function is ORGN.\n",
+       "10. ORGN, a list containg a comment indicating the origin of the object.\n",
+       "    This comment should be unique for a Kenzo session (between calls of\n",
+       "    CAT-INIT), as it is used for caching purposes. Its reader function\n",
+       "    is ORGN.\n",
        "-----------------------------------------------------------------------------\""
       ]
      },
@@ -152,11 +153,14 @@
        "Returns an instance of the class REDUCTION. The keyword arguments are as\n",
        "follows:\n",
        "\n",
-       ":F F, an object of type morphism representing the morphism f of a reduction\n",
+       ":F F, an object of type MORPHISM representing the chain morphism f of a\n",
+       "            reduction\n",
        "\n",
-       ":G G, an object of type morphism representing the morphism g of a reduction\n",
+       ":G G, an object of type MORPHISM representing the chain morphism g of a\n",
+       "            reduction\n",
        "\n",
-       ":H H, an object of type morphism representing the morphism h of a reduction\n",
+       ":H H, an object of type MORPHISM representing the morphism of graded modules h\n",
+       "            of a reduction\n",
        "\n",
        ":ORGN ORGN, a list containing a relevant and carefully chosen comment about\n",
        "            the origin of the chain complex. This comment should be unique\n",
@@ -1214,7 +1218,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 2.6 Construction of abicone from 2 reductions\n",
+    "## 2.6 Construction of a bicone from 2 reductions\n",
     "#### Example"
    ]
   },
@@ -2173,7 +2177,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 65,
    "metadata": {
     "collapsed": false
    },
@@ -2253,7 +2257,7 @@
        "NIL"
       ]
      },
-     "execution_count": 64,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/src/classes.lisp b/src/classes.lisp
index 8ca3a37..acba52e 100644
--- a/src/classes.lisp
+++ b/src/classes.lisp
@@ -326,21 +326,22 @@ The class has 7 slots:
 2. BCC, an object of type CHAIN-COMPLEX, the bottom chain complex C. Its reader
    function is BCC1.
 
-3. F, an object of type MORPHISM representing the morphism f. Its reader
+3. F, an object of type MORPHISM representing the chain morphism f. Its reader
    function is F1.
 
-4. G, an object of type MORPHISM representing the morphism g. Its reader
+4. G, an object of type MORPHISM representing the chain morphism g. Its reader
    function is G1.
 
-5. H, an object of type MORPHISM representing the morphism h. Its reader
-   function is H1.
+5. H, an object of type MORPHISM representing the morphism of graded modules h.
+   Its reader function is H1.
 
 9. IDNM, an integer, a system-generated identifier for this object. Its reader
    function is IDNM.
 
-10. ORGN, a list containg a comment indicating the origin of the object. The
-    should be unique (per session), since it is used in the implementation for
-    caching purposes. Its reader function is ORGN.
+10. ORGN, a list containg a comment indicating the origin of the object.
+    This comment should be unique for a Kenzo session (between calls of
+    CAT-INIT), as it is used for caching purposes. Its reader function
+    is ORGN.
 -----------------------------------------------------------------------------"))
 
 
diff --git a/src/effective-homology.lisp b/src/effective-homology.lisp
index 188dc1c..a99c24d 100644
--- a/src/effective-homology.lisp
+++ b/src/effective-homology.lisp
@@ -45,11 +45,14 @@ Args: (&key f g h orgn)
 Returns an instance of the class REDUCTION. The keyword arguments are as
 follows:
 
-:F F, an object of type morphism representing the morphism f of a reduction
+:F F, an object of type MORPHISM representing the chain morphism f of a
+            reduction
 
-:G G, an object of type morphism representing the morphism g of a reduction
+:G G, an object of type MORPHISM representing the chain morphism g of a
+            reduction
 
-:H H, an object of type morphism representing the morphism h of a reduction
+:H H, an object of type MORPHISM representing the morphism of graded modules h
+            of a reduction
 
 :ORGN ORGN, a list containing a relevant and carefully chosen comment about
             the origin of the chain complex. This comment should be unique