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# Sheaves on topoi: If E is a topos and S is an object in E, the category E < sub > S </ sub > of S-objects is also a topos, interpreted as the category of sheaves on S. If f: T → S is a morphism in E, the inverse image functor f < sup >*</ sup > can be described as follows: for a sheaf F on E < sub > S </ sub > and an object p: U → T in E < sub > T </ sub > one has f < sup >*</ sup > F ( U )
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# and Sheaves
# Sheaves on topological spaces: The inverse image functors of sheaves make the categories Sh ( S ) of sheaves on topological spaces S into a ( cleaved ) fibred category Sh over Top.
# and on
# Utilitarianism, where the practical consequences of various policies are evaluated on the assumption that the right policy will be the one which results in the greatest happiness
# Deontological ethics, notions based on ' rules ' i. e. that there is an obligation to perform the ' right ' action, regardless of actual consequences ( epitomized by Kant's notion of the Categorical Imperative )
# Various basic foodstuffs such as rice, sugar, wheat, cooking oil and butter ( the Salex Group enjoys a de facto monopoly on imports of wheat, sugar, flour, butter and cooking oil.
# election ( and condemnation on the day of judgment ) was conditioned by the rational faith or nonfaith of man ;
# If adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively ( like altitude on a contour map ), then as the eye moves towards the axes ( towards the south-west ), it sees the density of isotherms stay constant, but it sees the density of adiabats grow.
# REDIRECT Protocol on Environmental Protection to the Antarctic Treaty
# The unlawful act must be committed on board of an aircraft ( that is, by a person being on board of an aircraft, e. g. a passenger or crew member.
Per a News article on Page # 9 of the October 1984 issue of Acorn User, the Acorn ' Plus 2 ' interface was due to provide Econet capability.
Per a News article on Page # 9 of the October 1984 issue of Acorn User, the Plus 3 was originally destined to have used the Intel 8272 disk controller, ( and not 8271, which were in short supply at the time ).
# Abijah ( king ) of the Kingdom of Judah, also known as Abijam ( אבים ' aḄiYaM " My Father is Yam "), who was son of Rehoboam and succeeded him on the throne of Judah.
# HIV proteins decrease the amount of CD4 glycoprotein marker present on the cell membrane.
# discussion on mailing lists and at meetings ;
# The same asset does not trade at the same price on all markets (" the law of one price ").
# The Naturalization Act ( officially An act supplementary to, and to amend the act to establish a uniform rule of naturalization ; and to repeal the act heretofore passed on that subject ; ch.
# Katharina ( b. Meissen, 24 July 1468 – d. Göttingen, 10 February 1524 ), married firstly on 24 February 1484 in Innsbruck to Duke Sigismund of Austria, and secondly on 1497 to Duke Eric I of Brunswick-Calenberg.
It peaked at # 5 on the Billboard 200, and has been certified with a gold album by the RIAA.
In 2012, the album was ranked # 385 on Rolling Stone's 500 Greatest Albums of All Time, while Newsweek magazine pronounced it the second best album of its decade.
In 1997, the episode " Hedda Hopper's Hollywood " was ranked # 62 on TV Guide's 100 Greatest Episodes of All Time.
Flatt and Scruggs subsequently cut their own version of the theme ( with Flatt singing ) for Columbia Records ; released as a single, it reached # 44 on Billboard Hot 100 pop music chart and # 1 on the Billboard Hot Country chart ( the lone country chart-topper for the duo ).
" In December 2006, TV Guide even ranked the duo's distinct laughing at # 66 on their list of the 100 Greatest TV Quotes and Catchphrases.
# and If
# If P, then Q.
# If isotherms are concave towards the " north-east " direction ( 45 °), then adiabats are concave towards the " east north-east " ( 31 °).
# If morality is objective and absolute, God must exist.
# If the beat on the new record hits before the beat on the current record then the new record is too fast, reduce the pitch and manually slow the speed of the new record to bring the beats back in sync.
# If the beat on the new record hits after the beat on the current record then the new record is too slow, increase the pitch and manually increase the speed of the new record to bring the beats back in sync.
# It's Not Funny If I Have To Explain It — 2004 ; strips from 1997 to 2004, with more of Adams ' handwritten notes
# I Can't Remember If We're Cheap or Smart — 2012
# If equals are added to equals, then the wholes are equal.
# If equals are subtracted from equals, then the remainders are equal.
# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers ≤ N
# If the remainder is 2, swap 1 and 3 in odd list and move 5 to the end ( i. e. 3, 1, 7, 5 )
# If the remainder is 3, move 2 to the end of even list and 1, 3 to the end of odd list ( i. e. 4, 6, 8, 2-5, 7, 9, 1, 3 )
# If the design is symmetrical in an axis parallel to the flag pole, obverse and reverse will be identical despite the mirror-reversal, such as the Indian Flag or Canadian Flag
# If not, the obverse and reverse will present two variants of the same design, one with the hoist on the left ( usually considered the obverse side, see flag illustrations ), the other with the hoist on the right ( usually considered the reverse side of the flag ).
# If two straight lines in a plane are crossed by another straight line ( called the transversal ), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect ( also called the parallel postulate ).
# Associativity: If a * b and b * c are defined, then ( a * b ) * c and a * ( b * c ) are defined and equal.
# Identity: If a * b is defined, then a * b * b < sup >− 1 </ sup >
# If it persists, " gather facts and seek help.
# If the noun is animate, natural gender tends to dictate grammatical gender.
# If the borrowed word happens to have a suffix that the borrowing language uses as a gender marker, the suffix tends to dictate gender.
# If the borrowed word rhymes with one or more native words, the latter tend to dictate gender.
# If a project's spending becomes too much for a committee to continue funding, it must take the issue to the Project Committee.
# Affordable premium: If the likelihood of an insured event is so high, or the cost of the event so large, that the resulting premium is large relative to the amount of protection offered, it is not likely that the insurance will be purchased, even if on offer.
# If the German Armed Forces ( Wehrmacht ) were not in a position to break the danger from the Eastern front, then Nazi Germany would fall to Bolshevism, and all of Europe would fall shortly afterward ;
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