diff --git a/src/monggregate/pipeline.py b/src/monggregate/pipeline.py
index 7a19e78..539989f 100644
--- a/src/monggregate/pipeline.py
+++ b/src/monggregate/pipeline.py
@@ -315,7 +315,6 @@ def bucket(self, *, boundaries:list, by:Any=None, group_by:Any=None, default:Any
         self.stages.append(
             Bucket(
                 by = by or group_by,
-                #group_by = group_by or by,
                 boundaries = boundaries,
                 default = default,
                 output = output
@@ -372,7 +371,6 @@ def bucket_auto(self, *, by:Any=None, group_by:Any=None, buckets:int, output:dic
         self.stages.append(
             BucketAuto(
                 by = by or group_by,
-                #group_by = group_by,
                 buckets = buckets,
                 output = output,
                 granularity = granularity
@@ -438,9 +436,9 @@ def explode(self, \
 
         self.stages.append(
                 Unwind(
-                    path=path,
+                    path_to_array=path_to_array or path,
                     include_array_index=include_array_index,
-                    always=always
+                    always=always or preserve_null_and_empty_arrays
                     )
             )
         return self
@@ -453,7 +451,7 @@ def group(self, *,  by:Any|None=None, _id:Any|None=None, query:dict={})->Self:
         
         Arguments:
         ------------------------
-            - by,  str | list[str] | set[str] | dict | None : field or group of fields to group by
+            - by (_id),  str | list[str] | set[str] | dict | None : field or group of fields to group by
             - query, dict | None : Computed aggregated values (per group)
 
         Online MongoDB documentation:
@@ -475,7 +473,7 @@ def group(self, *,  by:Any|None=None, _id:Any|None=None, query:dict={})->Self:
 
         self.stages.append(
                 Group(
-                    by=by,
+                    by=by or _id,
                     query=query
                 )
             )
@@ -568,9 +566,9 @@ def lookup(self, *, \
             Lookup(
                 right = right,
                 on = on,
-                left_on = left_on,
-                right_on = right_on,
-                name =name
+                left_on = left_on or local_field, 
+                right_on = right_on or foreign_field,
+                name = name
             )
         )
         return self
@@ -713,7 +711,10 @@ def match(self, query:dict={}, expression:Any=None, **kwargs:Any)->Self:
 
         query = query | kwargs
         self.stages.append(
-                Match(query=query, expression=expression)
+                Match(
+                    query=query, 
+                    expression=expression
+                )
             )
         return self
 
@@ -797,7 +798,7 @@ def replace_root(self, path:str|None=None, path_to_new_root:str|None=None, *,doc
         -------------------------------------
 
             - statement, dict : the statement generated during instantiation after parsing the other arguments
-            - path_to_new_root, str|None : the path to the embedded document to be promoted
+            - path_to_new_root (path), str|None : the path to the embedded document to be promoted
             - document, dict|None : document being created and to be set as the new root or expression
 
         Online MongoDB documentation:
@@ -814,7 +815,10 @@ def replace_root(self, path:str|None=None, path_to_new_root:str|None=None, *,doc
         """
 
         self.stages.append(
-                ReplaceRoot(path=path, document=document)
+                ReplaceRoot(
+                    path=path or path_to_new_root, 
+                    document=document
+                )
             )
         return self
 
@@ -826,7 +830,7 @@ def replace_with(self, path:str|None=None, path_to_new_root:str|None=None, *,doc
         -------------------------------------
 
             - statement, dict : the statement generated during instantiation after parsing the other arguments
-            - path_to_new_root, str|None : the path to the embedded document to be promoted
+            - path_to_new_root (path), str|None : the path to the embedded document to be promoted
             - document, dict|None : document being created and to be set as the new root or expression
 
         Online MongoDB documentation:
@@ -843,7 +847,10 @@ def replace_with(self, path:str|None=None, path_to_new_root:str|None=None, *,doc
         """
 
         self.stages.append(
-                ReplaceRoot(path=path, document=document)
+                ReplaceRoot(
+                    path=path or path_to_new_root, 
+                    document=document
+                )
             )
         return self
 
@@ -1376,7 +1383,9 @@ def union_with(self, collection:str, coll:str, pipeline:list[dict]|None=None)->S
         """
 
         self.stages.append(
-            UnionWith(collection=collection, pipeline=pipeline)
+            UnionWith(
+                collection=collection or coll, 
+                pipeline=pipeline)
         )
 
         return self
diff --git a/src/monggregate/stages/group.py b/src/monggregate/stages/group.py
index 5e86587..4c51ad4 100644
--- a/src/monggregate/stages/group.py
+++ b/src/monggregate/stages/group.py
@@ -74,7 +74,7 @@ class Group(Stage):
 
     Attributes:
     -----------
-        - by,  str | list[str] | set[str] | dict | None : field or group of fields to group by
+        - by (_id),  str | list[str] | set[str] | dict | None : field or group of fields to group by
         - query, dict | None : Computed aggregated values (per group)
     
     Online MongoDB documentation:
diff --git a/src/monggregate/stages/replace_root.py b/src/monggregate/stages/replace_root.py
index 2b08c97..3b70356 100644
--- a/src/monggregate/stages/replace_root.py
+++ b/src/monggregate/stages/replace_root.py
@@ -77,7 +77,7 @@ class ReplaceRoot(Stage):
     -----------
 
         - statement, dict : the statement generated during instantiation after parsing the other arguments
-        - path_to_new_root, str|None : the path to the embedded document to be promoted
+        - path_to_new_root (path), str|None : the path to the embedded document to be promoted
         - document, dict|None : document being created and to be set as the new root or expression
     
     Online MongoDB documentation: