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Grothendieck universe
noun
(mathematics,
category
theory)
A
kind
of
universal
set
whose
elements
follow
the
rules
of
Zermelo–Fraenkel
set
theory,
and
for
which,
with
respect
to
an
arbitrary
set,
an
instance
of
its
kind
which
has
that
set
as
a
member
may
be
posited
to
exist
through
an
additional
Tarski–Grothendieck
axiom
(which
is
not
part
of
ZF
but
augments
it,
yielding
Tarski–Grothendieck
set
theory).
Grothendieck group
Grothendieck topology
noun
Ax-Grothendieck theorem
name
(mathematics)
A
result
about
injectivity
and
surjectivity
of
polynomials,
often
given
as
this
special
case:
If
P
is
an
injective
polynomial
function
from
an
n-dimensional
complex
vector
space
to
itself
then
P
is
bijective.
The
full
theorem
generalizes
to
any
algebraic
variety
over
an
algebraically
closed
field.
Grothendieck-Riemann-Roch theorem
name
Grothendieckian
adj
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