diff --git a/doc/library.rst b/doc/library.rst
index dbed4162..fe4ae000 100644
--- a/doc/library.rst
+++ b/doc/library.rst
@@ -124,5 +124,5 @@ What's new
 
 .. include::
    release.rst
-   :start-after: Release 0.5.0
-   :end-before: Release 0.4.0
+   :start-after: Release 0.5.1
+   :end-before: Release 0.5.0
diff --git a/doc/release.rst b/doc/release.rst
index 4d6e6c11..dfadafaf 100644
--- a/doc/release.rst
+++ b/doc/release.rst
@@ -4,6 +4,36 @@ Release Notes
 
 .. _stable:
 
+*************
+Release 0.5.1
+*************
+
+This release was made shortly after the release of version 0.5.0, to resolve an important bug. Please refer to `the release notes for 0.5.0 <https://giotto-ai.github.io/gtda-docs/0.5.0/release.html#release-0-5-0>`_ to see the major improvements and backwards-incompatible changes to the Mapper subpackage which were introduced there.
+
+Major Features and Improvements
+===============================
+
+None.
+
+Bug Fixes
+=========
+
+A bug preventing Mapper pipelines from working with memory caching has been fixed (`#597 <https://github.com/giotto-ai/giotto-tda/pull/597>`_).
+
+Backwards-Incompatible Changes
+==============================
+
+None.
+
+Thanks to our Contributors
+==========================
+
+This release contains contributions from:
+
+Umberto Lupo
+
+We are also grateful to all who filed issues or helped resolve them, asked and answered questions, and were part of inspiring discussions.
+
 *************
 Release 0.5.0
 *************
diff --git a/doc/versions b/doc/versions
index 095c0fbb..9d8bd668 100644
--- a/doc/versions
+++ b/doc/versions
@@ -5,4 +5,5 @@
 ./0.3.1
 ./0.4.0
 ./0.5.0
+./0.5.1
 ./latest
diff --git a/gtda/_version.py b/gtda/_version.py
index a5caaa70..32e32355 100644
--- a/gtda/_version.py
+++ b/gtda/_version.py
@@ -19,4 +19,4 @@
 # 'X.Y.dev0' is the canonical version of 'X.Y.dev'
 #
 
-__version__ = "0.5.0"
+__version__ = "0.5.1"
diff --git a/gtda/mapper/cluster.py b/gtda/mapper/cluster.py
index 9f9aa248..f8ce0944 100644
--- a/gtda/mapper/cluster.py
+++ b/gtda/mapper/cluster.py
@@ -16,6 +16,22 @@
 from ..utils.validation import validate_params
 
 
+def _sample_weight_computer(rel_indices, sample_weight):
+    return {"sample_weight": sample_weight[rel_indices]}
+
+
+def _empty_dict(*args):
+    return {}
+
+
+def _indices_computer_precomputed(rel_indices):
+    return np.ix_(rel_indices, rel_indices)
+
+
+def _indices_computer_not_precomputed(rel_indices):
+    return rel_indices
+
+
 class ParallelClustering(BaseEstimator):
     """Employ joblib parallelism to cluster different portions of a dataset.
 
@@ -129,16 +145,14 @@ def fit(self, X, y=None, sample_weight=None):
 
         fit_params = signature(self.clusterer.fit).parameters
         if sample_weight is not None and "sample_weight" in fit_params:
-            self._sample_weight_computer = lambda rel_indices, sample_weight: \
-                {"sample_weight": sample_weight[rel_indices]}
+            self._sample_weight_computer = _sample_weight_computer
         else:
-            self._sample_weight_computer = lambda *args: {}
+            self._sample_weight_computer = _empty_dict
 
         if self._precomputed:
-            self._indices_computer = lambda rel_indices: \
-                np.ix_(rel_indices, rel_indices)
+            self._indices_computer = _indices_computer_precomputed
         else:
-            self._indices_computer = lambda rel_indices: rel_indices
+            self._indices_computer = _indices_computer_not_precomputed
 
         # This seems necessary to avoid large overheads when running fit a
         # second time. Probably due to refcounts. NOTE: Only works if done
diff --git a/gtda/mapper/tests/test_cluster.py b/gtda/mapper/tests/test_cluster.py
index b457c543..9c6dde06 100644
--- a/gtda/mapper/tests/test_cluster.py
+++ b/gtda/mapper/tests/test_cluster.py
@@ -2,6 +2,9 @@
 for ParallelClustering."""
 # License: GNU AGPLv3
 
+from shutil import rmtree
+from tempfile import mkdtemp
+
 import numpy as np
 import pytest
 import sklearn as sk
@@ -11,7 +14,8 @@
 from numpy.testing import assert_almost_equal
 from scipy.spatial import distance_matrix
 
-from gtda.mapper import ParallelClustering, FirstHistogramGap, FirstSimpleGap
+from gtda.mapper import ParallelClustering, FirstHistogramGap, \
+    FirstSimpleGap, make_mapper_pipeline
 
 
 def test_parallel_clustering_bad_input():
@@ -233,3 +237,12 @@ def get_partition_from_preds(preds):
 
     assert get_partition_from_preds(preds) == \
            get_partition_from_preds(preds_mat)
+
+
+def test_mapper_pipeline_picklable():
+    # Regression test for issue #596
+    X = np.random.random((100, 2))
+    cachedir = mkdtemp()
+    pipe = make_mapper_pipeline(memory=cachedir)
+    pipe.fit_transform(X)
+    rmtree(cachedir)
diff --git a/setup.py b/setup.py
index 1fedb33d..700e8373 100755
--- a/setup.py
+++ b/setup.py
@@ -29,7 +29,7 @@
 MAINTAINER_EMAIL = "maintainers@giotto.ai"
 URL = "https://github.com/giotto-ai/giotto-tda"
 LICENSE = "GNU AGPLv3"
-DOWNLOAD_URL = "https://github.com/giotto-ai/giotto-tda/tarball/v0.5.0"
+DOWNLOAD_URL = "https://github.com/giotto-ai/giotto-tda/tarball/v0.5.1"
 VERSION = __version__  # noqa
 CLASSIFIERS = ["Intended Audience :: Science/Research",
                "Intended Audience :: Developers",