-
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...
- For
every signature σ,
induced substructures of σ-structures are the
subobjects in the
concrete category of σ-structures and
strong homomorphisms (and...
-
theorems that
describe the
relationship among quotients, homomorphisms, and
subobjects.
Versions of the
theorems exist for groups, rings,
vector spaces, modules...
- 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...
- X_{2}\subseteq \cdots } of
subobjects of X {\displaystyle X}
eventually becomes stationary. This is the case if and only if
every subobject of X is
finitely generated...
-
elements of the
subobject classifier. In particular, in a
topos every formula of higher-order
logic may be ****igned a
truth value in the
subobject classifier...
-
called the
image of f.
Subobjects and
quotient objects are well-behaved in
abelian categories. For example, the
poset of
subobjects of any
given object A...
