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regular sketch, 274, 283 stable images, 242
regular theory, 275 stable sups, 242
regularly co-well-powered, 303 stable under pullback, 48
representable functor, 27 stalk, 81
restriction map, 77 standard, 227, 262
retraction, 21 strict, 186
right exact, 48 strict initial object, 228
structure map, 103
saturated, 224, 234 subcanonical, 227
section of, 242 subcategory, 2
sections, 78 subfunctor, 25
separable, 262 subobject, 23, 32
separated object, 201 subobject classi¬er, 87, 177
separator, 289 sum, 47
Set, 1 support, 242
set of sorts, 155 supports split, 242
sheaf, 77, 196, 202, 205
sheaf of sections, 78 target, 1, 35
shea¬¬cation, 82, 202 terminal object, 4
sheaves, 98 theory, vii, 274
Sierpinski space, 191 Top, 1
sieve, 223, 274 topology, 195
simplicial object, 222 topos, vii, 74, 79, 165, 208, 215, 221
single-sorted, 154 torsion theories , 197
singleton, 88 total, 233
Singleton set, 4 total space, 81
site, 224 transpose, 54
skeleton, 10 triple, vii, 96
sketch, 144 tripleable, 107, 116, 155, 288, 289, 293
slice, 172 twisted arrow category of, 9
slice category, 3
ultra¬lter, 282
small, 1
ultraproduct, 282
solution set condition, 58
under, 5
source, 1, 35
underlying graph, 35
split, 109
underlying graph functor, 35
split discrete op¬bration, 219
underlying set functor, 11
split epi, 242
underlying sketch, 145
split epimorphism, 21
328 Index
union, 184
unique lifting property, 219
unit, 55
universal, 224, 225
universal arrow, 58
universal element, 27
upper semilattice, 15

VTT, 126
Vulgar Tripleability Theorem, 126

weak universal arrow, 58
well powered, 65
well-pointed, 238

Yoneda, 27
Yoneda embedding, 25, 26, 233
Yoneda map, 25, 26

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