-
monomorphisms are the
subobjects of A{\displaystyle A}. The
relation ≤
induces a
partial order on the
collection of
subobjects of A{\displaystyle A}....
- In
category theory, a
subobject classifier is a
special object Ω of a
category such that, intuitively, the
subobjects of any
object X in the category...
-
chain condition on
certain kinds of
subobjects,
meaning that
certain ascending or
descending sequences of
subobjects must have
finite length. Noetherian...
- and n are equivalent. The
subobjects of X are the
resulting equivalence classes of the
monics to it. In a
topos "
subobject" becomes, at
least implicitly...
- has two
different Animal base
class subobjects. So, an
attempt to
directly bind a
reference to the
Animal subobject of a Bat
object would fail,
since the...
- that
describe the
relationship between quotients, homomorphisms, and
subobjects.
Versions of the
theorems exist for groups, rings,
vector spaces, modules...
- the
empty set. This
latter set is
important in
category theory: it is a
subobject classifier in the
category of sets. More broadly, a set that is a field...
-
generalization of a topos. A
topos has a
subobject classifier classifying all
subobjects, but in a quasitopos, only
strong subobjects are classified. Quasitoposes...
- {\displaystyle r} -coloring of all
subobjects of C {\displaystyle C}
isomorphic to A {\displaystyle A}
there exists a
monochromatic subobject isomorphic to B {\displaystyle...
- the
domain of a
double integral. In
topos theory, the (codomain of the)
subobject classifier of an
elementary topos. In
combinatory logic, the
looping combinator...
