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diff --git a/topics/_week7_monads.mdwn b/topics/_week7_monads.mdwn
index 21ac2f59..75bc2051 100644
--- a/topics/_week7_monads.mdwn
+++ b/topics/_week7_monads.mdwn
@@ -1,3 +1,5 @@
+<!-- λ Λ ∀ ≡ α β ρ ω Ω -->
+
 Monads
 ======
 
@@ -8,10 +10,43 @@ monsters, monads are burritos.  We're part of the backlash that
 prefers to say that monads are monads.  
 
 The closest we will come to metaphorical talk is to suggest that
-monadic types place objects inside of boxes, and that monads wrap and
-unwrap boxes to expose or enclose the objects inside of them.  In any
-case, the emphasis will be on starting with the abstract structure of
-monads, followed by instances of monads from the philosophical and
+monadic types place objects inside of *boxes*, and that monads wrap
+and unwrap boxes to expose or enclose the objects inside of them.  In
+any case, the emphasis will be on starting with the abstract structure
+of monads, followed by instances of monads from the philosophical and
 linguistics literature.
 
-To 
+### Boxes: type expressions with one free type variable
+
+Recall that we've been using lower-case Greek letters
+<code>&alpha;, &beta;, &gamma;, ...</code> to represent types.  We'll
+use `P`, `Q`, `R`, and `S` as metavariables over type schemas, where a
+type schema is a type expression that may or may not contain unbound
+type variables.  For instance, we might have
+
+    P ≡ Int
+    P ≡ α -> α
+    P ≡ ∀α. α -> α
+    P ≡ ∀α. α -> β 
+
+etc.
+
+A box type will be a type expression that contains exactly one free
+type variable.  Some examples (using OCaml's type conventions):
+
+    α Maybe
+    α List
+    (α, P) Tree    (assuming P contains no free type variables)
+    (α, α) Tree
+
+The idea is that whatever type the free type variable α might be,
+the boxed type will be a box that "contains" an object of type α.
+For instance, if `α List` is our box type, and α is the basic type
+Int, then in this context, `Int List` is the type of a boxed integer.
+
+We'll often write box types as a box containing the value of the free
+type variable.  So if our box type is `α List`, and `α == Int`, we
+would write
+
+<table border=2px><td>Int</td></table>
+