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natural numbers object
noun
(category
theory)
An
object
which
has
a
distinguished
global
element
(which
may
be
called
z,
for
“zero”)
and
a
distinguished
endomorphism
(which
may
be
called
s,
for
“successor”)
such
that
iterated
compositions
of
s
upon
z
(i.e.,
sⁿ∘z)
yields
other
global
elements
of
the
same
object
which
correspond
to
the
natural
numbers
(sⁿ∘z↔n).
Such
object
has
the
universal
property
that
for
any
other
object
with
a
distinguished
global
element
(call
it
z’)
and
a
distinguished
endomorphism
(call
it
s’),
there
is
a
unique
morphism
(call
it
φ)
from
the
given
object
to
the
other
object
which
maps
z
to
z’
(𝜙∘z=z')
and
which
commutes
with
s;
i.e.,
𝜙∘s=s'∘𝜙.
scattered disc object
massive compact halo object
noun
massive astrophysical compact halo object
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