name
Name:
Level: Level modification
Description:

short_exact_sequence_of
Name: Short exact sequence of \ldots
Level: Multiplies level of monster by three
Description: 

long_exact_sequence_of
Name: Long exact sequence of \ldots
Level: Multiplies level of monster by $\aleph_0$
Description: 

localization
Name: \ldots and its localization
Level: Doubles the level of monster
Description:

pathological
Name: Pathological \ldots
Level: +10 to level of monster
Description:

almost_everywhere
Name: \ldots almost everywhere
Description: The monster is everywhere except a finite number of places.  The chance that you are able to run to one of those places is infinitesimally small, so you cannot run away from the monster.

uncountably_infinite
Name: Uncountably infinite \ldots
Level: +10 to level of monster
Description: 

well_ordered
Name: Well-ordered \ldots
Level: -5 to level of monster
Description: 

canonical
Name: Canonical \ldots
Level: +5 to level of monster
Description:

deep
Name: Deep \ldots
Level: +5 to level of monster
Description:

elementary
Name: Elementary \ldots
Level: -5 to level of monster
Description:

smooth
Name: Smooth \ldots
Description: If an analysist is fighting a smooth monster, he/she may choose to differentiate it infinitely many times, making it disappear, instead of fighting it.

conjectured
Name: Conjectured \ldots
Description: Noone has proved that this monster exists.  If you do not believe in it, you do not have to fight it.