- 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...
- 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...
- exist. The
category has a
subobject classifier. The
category is
Cartesian closed. In some applications, the role of the
subobject classifier is pivotal,...
-
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...
-
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...
-
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...
- of
rings Category of
magmas Initial object Terminal object Zero
object Subobject Group object Magma object Natural number object Exponential object Epimorphism...
- 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...
-
theorems that
describe the
relationship among quotients, homomorphisms, and
subobjects.
Versions of the
theorems exist for groups, rings,
vector spaces, modules...
- _{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...
