- In
category theory, a
branch of mathematics, a
subobject is,
roughly speaking, an
object that sits
inside another object in the same category. The notion...
- exist. The
category has a
subobject classifier. The
category is
Cartesian closed. In some applications, the role of the
subobject classifier is pivotal,...
-
especially 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...
-
useful for
multiple inheritance, as it
makes the
virtual base a
common subobject for the
deriving class and all
classes that are
derived from it. This...
-
object B′, and this
homomorphism induces an
isomorphism from a
subobject A of B to a
subobject A′ of B′ and also an
isomorphism from the
factor object B/A...
- the
result value recursively computed from each
recursive subobject, but the
original subobject itself as well.
Example Haskell implementation, for lists:...
-
property of an
object that is
inherited by all of its
subobjects,
where the
meaning of
subobject depends on the context.
These properties are particularly...
-
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...
-
chain condition on
certain kinds of
subobjects,
meaning that
certain ascending or
descending sequences of
subobjects must have
finite length. Noetherian...
- _{s}}
defines another subobject s ¯ : S ¯ ↣ A {\displaystyle {\bar {s}}:{\bar {S}}\rightarrowtail A} of A such that s is a
subobject of s ¯ {\displaystyle...
