diff --git a/examples/Chapter13.ipynb b/examples/Chapter13.ipynb
index 779105b..6974c36 100644
--- a/examples/Chapter13.ipynb
+++ b/examples/Chapter13.ipynb
@@ -10,7 +10,7 @@
     "\n",
     "Let us recall the definition of the  *free group* generated by a set ${\\cal A}$. Consider the set ${\\cal A}\\times \\lbrace +1, -1 \\rbrace$ and make, as long as there is no ambiguity, the identification $a_i= (a_i,1)$ and $a_i^{-1}= (a_i,-1)$ for all $a_i\\in{\\cal A}$.\n",
     "\n",
-    "**Definition.**  $a_i$ and its formal inverse $a_i^{-1}$ are  {\\em letters}.\n",
+    "**Definition.**  $a_i$ and its formal inverse $a_i^{-1}$ are *letters*.\n",
     "\n",
     "**Definition.** A word is a *finite* sequence of letters, possibly repeated, without any pair of the form $a_ja_j^{-1}$ and $a_k^{-1}a_k$. The word is said *reduced*.\n",
     "\n",
@@ -148,44 +148,88 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<<Loop>>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(loop3)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<<Loop[A\\2][4-2 B\\-3][3-2 C]>>"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(loop3 0 'a 2 20 'b -3 12 'c 1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<<Loop[A\\2][4-2 B\\-3][3-2 C][A\\3]>>"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(loop3 0 'a 2 20 'b -3 12 'c 1 0 'a 3)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<<Loop[2-1-0 P\\2][5-4-3-2-1 Q\\5]>>"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(loop3 (dgop-ext-int '(2 1 0)) 'p 2 \n",
     "       (dgop-ext-int '(5 4 3 2 1)) 'q 5)"
@@ -201,22 +245,71 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K1 Simplicial-Set]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def moore23 (moore 2 3))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "\n",
+      "Dimension = 0:\n",
+      "\n",
+      "       Vertices :  (*)\n",
+      "\n",
+      "Dimension = 1:\n",
+      "\n",
+      "Dimension = 2:\n",
+      "\n",
+      "Dimension = 3:\n",
+      "\n",
+      "       Simplex : M3\n",
+      "\n",
+      "               Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
+      "\n",
+      "Dimension = 4:\n",
+      "\n",
+      "       Simplex : N4\n",
+      "\n",
+      "               Faces : (<AbSm - M3> <AbSm 2-1-0 *> <AbSm - M3> <AbSm 2-1-0 *> <AbSm 2-1-0 *>)"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(show-structure moore23 4)"
    ]
@@ -230,66 +323,132 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K6 Simplicial-Group]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def o-moore23 (loop-space moore23))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm 2-1-0 <<Loop>>>"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-moore23 0 4 +null-loop+)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[M3\\2]>>>"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-moore23 0 3 (loop3 0 'N4 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm 1-0 <<Loop>>>"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-moore23 1 3 (loop3 0 'N4 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[N4\\2]>>>"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-moore23 1 4 (loop3 1 'N4 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm 0 <<Loop>>>"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-moore23 0 2 (loop3 0 'M3 2))"
    ]
@@ -303,11 +462,46 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "The object is a STANDARD-OBJECT of type CAT::SIMPLICIAL-SET.\n",
+      "0. CMPR: #<FUNCTION S-CMPR>\n",
+      "1. BASIS: #<CLOSURE (FLET CAT::RSLT :IN CAT::FINITE-SS-BASIS) {1005791FCB}>\n",
+      "2. BSGN: *\n",
+      "3. DFFR: [K19 Morphism (degree -1): K18 -> K18]\n",
+      "4. GRMD: [K18 Simplicial-Set]\n",
+      "5. EFHM: \"unbound\"\n",
+      "6. IDNM: 18\n",
+      "7. ORGN: (BUILD-FINITE-SS (* 2 S2 (* * *) 3 S3 (S2 S2 S2 S2)))\n",
+      "8. CPRD: [K22 Morphism (degree 0): K18 -> K20]\n",
+      "9. FACE: #<CLOSURE (FLET CAT::RSLT :IN CAT::FINITE-SS-FACE) {1005791FEB}>\n",
+      "\n",
+      "> \n",
+      "Checking the 0-simplices...\n",
+      "Checking the 1-simplices...\n",
+      "Checking the 2-simplices...\n",
+      "Checking the 3-simplices..."
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[K18 Simplicial-Set]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def ss2 (build-finite-ss '( * \n",
     "                              2 s2 (* * *) \n",
@@ -316,110 +510,220 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K23 Simplicial-Group]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def o-ss2 (loop-space ss2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop>>>"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-ss2 0 1 (loop3 0 's2 1))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[S2\\2]>>>"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-ss2 0 2 (loop3 0 's3 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[S2\\2]>>>"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-ss2 1 2 (loop3 0 's3 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[S2\\2]>>>"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face o-ss2 1 2 (loop3 0 's3 2))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K40 Simplicial-Group]"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def db (gdeltab))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm 1-0 <<Loop>>>"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face db 3 3 (loop3 12 7 3))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm 0 <<Loop[7\\3]>>>"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face db 3 3 (loop3 5 7 3))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[1 7\\3][0 7\\3][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5]>>>"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face db 3 3 (loop3 6 7 3 5 7 3 3 7 3))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<AbSm - <<Loop[7\\3][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5]>>>"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(face db 3 2 *)"
    ]
@@ -433,11 +737,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 1}\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(? db (? db 3 (loop3 (dgop-ext-int '(3 2)) (dlop-ext-int '(0 1 2)) 3\n",
     "                     (dgop-ext-int '(3 1)) (dlop-ext-int '(0 1 2)) 3\n",
@@ -453,66 +770,154 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K52 Simplicial-Set]"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def moore-22 (moore 2 2)) "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "(<AbSm - *>) \n",
+      "(<AbSm 0 *>) \n",
+      "(<AbSm - M2> <AbSm 1-0 *>) \n",
+      "(<AbSm - N3> <AbSm 0 M2> <AbSm 1 M2> <AbSm 2 M2> <AbSm 2-1-0 *>) "
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(dotimes (i 4) (print (basis moore-22  i :dgnr)))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K57 Simplicial-Group]"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def o-moore-22 (loop-space moore-22))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<1 * <<Loop[1-0 M2][2 N3]>>>\n",
+       "<-1 * <<Loop[2-0 M2][1 N3]>>>\n",
+       "<1 * <<Loop[2-1 M2][0 N3]>>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(aprd o-moore-22 3 (tnpr 1 (loop3 0 'm2 1) 2 (loop3 0 'n3 1)))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K74 Chain-Complex]"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(def bar-om (bar o-moore-22))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 4}\n",
+       "<1 * <<Abar[4 <<Loop[1-0 M2][2 N3]>>]>>>\n",
+       "<-1 * <<Abar[4 <<Loop[2-0 M2][1 N3]>>]>>>\n",
+       "<1 * <<Abar[4 <<Loop[2-1 M2][0 N3]>>]>>>\n",
+       "<-2 * <<Abar[2 <<Loop[M2]>>][2 <<Loop[M2]>>]>>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "(? bar-om 5 (abar 2 (loop3 0 'm2 1) 3 (loop3 0 'n3 1)))"
    ]