diff --git a/cubed/array_api/array_object.py b/cubed/array_api/array_object.py
index b3e8abe9..d7363241 100644
--- a/cubed/array_api/array_object.py
+++ b/cubed/array_api/array_object.py
@@ -399,12 +399,18 @@ def __int__(self, /):
     # Utility methods
 
     def _check_allowed_dtypes(self, other, dtype_category, op):
-        if self.dtype not in _dtype_categories[dtype_category]:
+        if (
+            dtype_category != "all"
+            and self.dtype not in _dtype_categories[dtype_category]
+        ):
             raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
         if isinstance(other, (int, complex, float, bool)):
             other = self._promote_scalar(other)
         elif isinstance(other, CoreArray):
-            if other.dtype not in _dtype_categories[dtype_category]:
+            if (
+                dtype_category != "all"
+                and other.dtype not in _dtype_categories[dtype_category]
+            ):
                 raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
         else:
             return NotImplemented
diff --git a/cubed/array_api/statistical_functions.py b/cubed/array_api/statistical_functions.py
index 78ff6ae2..7ee6525e 100644
--- a/cubed/array_api/statistical_functions.py
+++ b/cubed/array_api/statistical_functions.py
@@ -1,6 +1,7 @@
 import math
 
 from cubed.array_api.dtypes import (
+    _boolean_dtypes,
     _numeric_dtypes,
     _real_floating_dtypes,
     _real_numeric_dtypes,
@@ -124,10 +125,13 @@ def min(x, /, *, axis=None, keepdims=False, use_new_impl=True, split_every=None)
 def prod(
     x, /, *, axis=None, dtype=None, keepdims=False, use_new_impl=True, split_every=None
 ):
-    if x.dtype not in _numeric_dtypes:
-        raise TypeError("Only numeric dtypes are allowed in prod")
+    # boolean is allowed by numpy
+    if x.dtype not in _numeric_dtypes and x.dtype not in _boolean_dtypes:
+        raise TypeError("Only numeric or boolean dtypes are allowed in prod")
     if dtype is None:
-        if x.dtype in _signed_integer_dtypes:
+        if x.dtype in _boolean_dtypes:
+            dtype = int64
+        elif x.dtype in _signed_integer_dtypes:
             dtype = int64
         elif x.dtype in _unsigned_integer_dtypes:
             dtype = uint64
@@ -153,10 +157,13 @@ def prod(
 def sum(
     x, /, *, axis=None, dtype=None, keepdims=False, use_new_impl=True, split_every=None
 ):
-    if x.dtype not in _numeric_dtypes:
-        raise TypeError("Only numeric dtypes are allowed in sum")
+    # boolean is allowed by numpy
+    if x.dtype not in _numeric_dtypes and x.dtype not in _boolean_dtypes:
+        raise TypeError("Only numeric or boolean dtypes are allowed in sum")
     if dtype is None:
-        if x.dtype in _signed_integer_dtypes:
+        if x.dtype in _boolean_dtypes:
+            dtype = int64
+        elif x.dtype in _signed_integer_dtypes:
             dtype = int64
         elif x.dtype in _unsigned_integer_dtypes:
             dtype = uint64
diff --git a/cubed/tests/test_types.py b/cubed/tests/test_types.py
new file mode 100644
index 00000000..b21eca6e
--- /dev/null
+++ b/cubed/tests/test_types.py
@@ -0,0 +1,10 @@
+from numpy.testing import assert_array_equal
+
+import cubed.array_api as xp
+
+
+# This is less strict than the spec, but is supported by implementations like NumPy
+def test_prod_sum_bool():
+    a = xp.ones((2,), dtype=xp.bool)
+    assert_array_equal(xp.prod(a).compute(), xp.asarray([1], dtype=xp.int64))
+    assert_array_equal(xp.sum(a).compute(), xp.asarray([2], dtype=xp.int64))