- theoretically) A
poset is a (small, thin, and skeletal)
category such that each
homset has at most one element. An
order embedding A → B is a full and faithful...
-
category theory, a
posetal category, or thin category, is a
category whose homsets each
contain at most one morphism. As such, a
posetal category amounts...
- that for all
objects a and b, the hom-class hom(a, b) is a set,
called a
homset. Many
important categories in
mathematics (such as the
category of sets)...
-
program P, the
homsets of the
fundamental category of X are countable. In addition, if no
looping instruction occurs in P, then the
homsets of X are finite...
- integers. (In many texts, it is
written instead as hom([n],-)
where the
homset is
understood to be in the
opposite category Δop.) By the
Yoneda lemma,...
- *-autonomous with
dualizer the
chain of two elements. A
degenerate example (all
homsets of
cardinality at most one) is
given by any
Boolean algebra (as a partially...
- be
axiomatised as a
Frobenius algebra, the cuts are
unary operators on
homsets that
axiomatise logical negation. This
makes string diagrams a
sound and...
-
enriched category based on
intuitions then in the air
about making the
homsets of a
category just as
abstract as the
objects themselves.[citation needed]...
