diff --git a/pytensor/tensor/random/op.py b/pytensor/tensor/random/op.py
index 597f68865d..6f7d8ad438 100644
--- a/pytensor/tensor/random/op.py
+++ b/pytensor/tensor/random/op.py
@@ -191,7 +191,7 @@ def extract_batch_shape(p, ps, n):
                 return shape
 
             batch_shape = [
-                s if b is False else constant(1, "int64")
+                s if not b else constant(1, "int64")
                 for s, b in zip(shape[:-n], p.type.broadcastable[:-n])
             ]
             return batch_shape
diff --git a/pytensor/tensor/type.py b/pytensor/tensor/type.py
index ef55d2bf75..7e56fc53e3 100644
--- a/pytensor/tensor/type.py
+++ b/pytensor/tensor/type.py
@@ -109,8 +109,13 @@ def __init__(
         def parse_bcast_and_shape(s):
             if isinstance(s, (bool, np.bool_)):
                 return 1 if s else None
-            else:
+            elif isinstance(s, (int, np.int_)):
+                return int(s)
+            elif s is None:
                 return s
+            raise ValueError(
+                f"TensorType broadcastable/shape must be a boolean, integer or None, got {type(s)} {s}"
+            )
 
         self.shape = tuple(parse_bcast_and_shape(s) for s in shape)
         self.dtype_specs()  # error checking is done there
diff --git a/tests/tensor/random/test_basic.py b/tests/tensor/random/test_basic.py
index adc4177085..10da939d07 100644
--- a/tests/tensor/random/test_basic.py
+++ b/tests/tensor/random/test_basic.py
@@ -16,6 +16,7 @@
 from pytensor.graph.op import get_test_value
 from pytensor.graph.replace import clone_replace
 from pytensor.graph.rewriting.db import RewriteDatabaseQuery
+from pytensor.tensor import ones, stack
 from pytensor.tensor.random.basic import (
     _gamma,
     bernoulli,
@@ -1465,3 +1466,12 @@ def test_rebuild():
     assert y_new.type.shape == (100,)
     assert y_new.shape.eval({x_new: x_new_test}) == (100,)
     assert y_new.eval({x_new: x_new_test}).shape == (100,)
+
+
+def test_categorical_join_p_static_shape():
+    """Regression test against a bug caused by misreading a numpy.bool_"""
+    p = ones(3) / 3
+    prob = stack([p, 1 - p], axis=-1)
+    assert prob.type.shape == (3, 2)
+    x = categorical(p=prob)
+    assert x.type.shape == (3,)
diff --git a/tests/tensor/test_basic.py b/tests/tensor/test_basic.py
index aea96365e1..2c2b82d1b5 100644
--- a/tests/tensor/test_basic.py
+++ b/tests/tensor/test_basic.py
@@ -2046,8 +2046,14 @@ def test_mixed_ndim_error(self):
     def test_static_shape_inference(self):
         a = at.tensor(dtype="int8", shape=(2, 3))
         b = at.tensor(dtype="int8", shape=(2, 5))
-        assert at.join(1, a, b).type.shape == (2, 8)
-        assert at.join(-1, a, b).type.shape == (2, 8)
+
+        res = at.join(1, a, b).type.shape
+        assert res == (2, 8)
+        assert all(isinstance(s, int) for s in res)
+
+        res = at.join(-1, a, b).type.shape
+        assert res == (2, 8)
+        assert all(isinstance(s, int) for s in res)
 
         # Check early informative errors from static shape info
         with pytest.raises(ValueError, match="must match exactly"):
@@ -2055,8 +2061,9 @@ def test_static_shape_inference(self):
 
         # Check partial inference
         d = at.tensor(dtype="int8", shape=(2, None))
-        assert at.join(1, a, b, d).type.shape == (2, None)
-        return
+        res = at.join(1, a, b, d).type.shape
+        assert res == (2, None)
+        assert isinstance(res[0], int)
 
     def test_split_0elem(self):
         rng = np.random.default_rng(seed=utt.fetch_seed())
diff --git a/tests/tensor/test_type.py b/tests/tensor/test_type.py
index 4e9c456829..e80ee47637 100644
--- a/tests/tensor/test_type.py
+++ b/tests/tensor/test_type.py
@@ -267,6 +267,27 @@ def test_fixed_shape_basic():
     assert t2.shape == (2, 4)
 
 
+def test_shape_type_conversion():
+    t1 = TensorType("float64", shape=np.array([3], dtype=int))
+    assert t1.shape == (3,)
+    assert isinstance(t1.shape[0], int)
+    assert t1.broadcastable == (False,)
+    assert isinstance(t1.broadcastable[0], bool)
+
+    t2 = TensorType("float64", broadcastable=np.array([True, False], dtype="bool"))
+    assert t2.shape == (1, None)
+    assert isinstance(t2.shape[0], int)
+    assert t2.broadcastable == (True, False)
+    assert isinstance(t2.broadcastable[0], bool)
+    assert isinstance(t2.broadcastable[1], bool)
+
+    with pytest.raises(
+        ValueError,
+        match="TensorType broadcastable/shape must be a boolean, integer or None",
+    ):
+        TensorType("float64", shape=("1", "2"))
+
+
 def test_fixed_shape_clone():
     t1 = TensorType("float64", (1,))