Category Theory II
Corrections to Proofs

PLEASE NOTE: "Extra text" in chapter 8 *is* to be included.

Front Matter

i. insert "S." to read "D.S. Scott" (that has been approved by series editor).
ii. capitalization in book titles is inconsistent -- consult editor.
x, line 28: insert "$\lambda$-" to read "$\lambda$-calculus"
x, line 30: replace "two" by "2"
x, line -1: should read Figures 9.1 and 8.1.
xiv, line -10: lowercase "Lemma".
xiv, line -9: lowercase "Lemma".
search text for "Yoneda Lemma" and lowercase "Lemma"
xv, line 4: l.c. "Preserve"

Chapter 1

3, line 8: replace "in" with "on"
6, line 2: replace "finite or infinite?" with "finite? infinite?"
6, line 18: delete "and"
7, line 14: change period "." to a comma ","
9, line 4: delete commas before and after "thus"
10, line 19: delete the first (unitalicized) occurrence of "category" and it's comma.
10, line -2: delete "and"
12 AQ: yes, expand "resp." to "respectively,"
15, line 7: make "C" bf roman by using the command $\C$

Chapter 2

29, line -5: insert "a"
36: change "for" to "of"
46 AQ: example 10 of Section 1.4
46 (half page): delete commas before and after "thus"
52, line 2: change "," to "."

Chapter 3

55: top, insert we "shall" see.
60: prop. 3.11, add index entry: product, abelian groups
65: insert a period "." into the second display
66: insert a period "." after "Z" in the last displayed diagram
68: insert a period "." into the 1st, 2nd, 4th, and 5th displays.
70 AQ: OK as set (but not as stated in the AQ).
70, line -6: insert colon ":"

Chapter 4

79: Def. 4.9: monoidal category: the index entry shows p. 80 rather than p. 79.
	also, please add index entry: monoidal category, see category, monoidal.
82: insert "the following diagram."
86 AQ: yes, example 3.22 is correct.

Chapter 5

89: change "through" to "via"
91: insert a period "." into displays 7 and 8.
111 AQ: change "example" to "proposition 3.11".

Chapter 6

119, line 6: delete "(UMPs)"
119, line -3: replace f_a(y) by f(a,y).
120, line 11: delete commas before and after "thus"
121: replace "it states" by "we have"
122 AQ: yes, CCC = cartesian closed category
124 AQ: insert "so" to read "if f is so".
131, line 13: delete "(IPC)"
131, line 18: insert "intuitionistic propositional calculus" before "(IPC)"
133, line 18: delete paren.s around "HA"
133, line -2: insert "the Heyting algebra"
134, line 11: spell out "intuitionistic propositional calculus" in place of "IPC"
135, line -7: spell out "intuitionistic propositional calculus" in place of "IPC"
136, line 5: change "There" to "They"
138, 3rd display: add a period "."
140, line 15, orphan "p".
144, line 15: change "this" to "the following"

Chapter 7

151, line -5: change "that" back to "which"
162, line 7: replace "(of lemma)." by "(Lemma)" -- note no punctuation
163: first displayed diagram, insert some vspace before.
163, line 3: replace "(of proposition):" by "(Proposition)" -- note no punctuation
166, line -3: delete "s" to read "form"
168 AQ: section 4.1
171: change "cute limination" to "cut elimination"
176, line 3: insert colon
176: too much vspace before and after prop. 7.28.
	the whole page seems to have too much vspace.
181: Johnston --> Johnstone, and insert a period "."

Chapter 8

185, line -7: the expression Sets^{Sets_{fin}} contains a spurious comma: delete.
185, line -6: delete another comma
186, line 7: change "were" to "was"
188, line -4: lowercase "Lemma"
193, line 1: lowercase "Lemma"
193, line 14: delete "UMP, "
194, line 19: change the m-dash "---" to a comma ","
196, line -6: change comma "," to period "."
198, line 18: change roman back to ital.
199, line -11: change "this exercise" to "exercise 7 of Chapter 7"
205: insert the following new exercise between numbers 9 and 10 (and allow the subsequent ones to be renumbered): 
	\item Combine proposition 6.17 with theorem 8.14 to infer that the $\lambda$-calculus is deductively complete with respect to categories of diagrams.\index{lambda-calculus}

Chapter 9

207, line 5: delete "to" in "applies to everything" to read "applies everything"
207, line 6: delete "(UMPs)"
207, line 9: insert "will"
207, line -9: change "UMP" to "universal mapping property (UMP)"
222, line 15: change "the above-mentioned" to "this"
215: add period in display before 9.3.
224: figure 9.1 is missing!  the file fig2.eps included with this email.
225, line 7: change "Right adjoints Preserve limits (RAPL)" back to simply "RAPL"
225, line -9: change "RAPL" to "Right adjoints preserve limits (RAPL!)"
231 AQ: the change is *not* correct.  The sentence should read: "An arbitrary such function between ..."
237 AQ: yes, thm 8.14 is correct.
237 AQ: revise to read: "as was shown in exercise 10 of chapter 8."
243, line 13: change "set" to "calculation"
243 AQ: change to "nullary" OK.
245, line -1: delete "(NNO)"
246, line 1: change "An NNO" to "A natural numbers object (NNO)"
249, line 10: delete "or"

Chapter 10

253, line -3: replace "set" by "consideration" 
255, line -12: replace "question." by a colon ":"
269, line 5: insert "zero"
269, line 12: too much vspace?
271, line 18: delete "(UMP)"
272. line -14: change "has" to "have"
277, line 14: insert "to be"

Back Matter

280 AQ: yes, sequence is OK.
281, lower halfpage: move the display to the right.
282, line -16: change "universal mapping property (UMP)" to "UMP"

298: renumber (chapter 8) solution 11 to 12.
301 AQ: in the displayed box, line 2. second occurrence of "b" should be math ital, like the nearby letters.
	also, 4th line insert period after "t" to read "s.t."
303: line 11: change "Introduciton" to "Introduction"
303: line -3: insert 2 commas to read  "Berlin, Heidelberg, New York."