- 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...
- 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...
- 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...
-
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...
-
special sense: the
truth values of a
topos are the
global elements of the
subobject classifier.
Having truth values in this
sense does not make a
logic truth...
- r{\displaystyle r}-coloring of all
subobjects of C{\displaystyle C}
isomorphic to A{\displaystyle A}
there exists a
monochromatic subobject isomorphic to B{\displaystyle...
- of
rings Category of
magmas Initial object Terminal object Zero
object Subobject Group object Magma object Natural number object Exponential object Epimorphism...
