diff --git a/src/ACSetInterface.jl b/src/ACSetInterface.jl
index e78fda1..9dfaccf 100644
--- a/src/ACSetInterface.jl
+++ b/src/ACSetInterface.jl
@@ -1,10 +1,11 @@
 module ACSetInterface
-export ACSet, acset_schema, acset_name, dom_parts, subpart_type,
+export ACSet, acset_schema, acset_name, dom_parts, codom_parts, subpart_type,
   nparts, maxpart, parts, has_part, has_subpart, subpart, incident,
   add_part!, add_parts!, set_subpart!, set_subparts!, clear_subpart!,
   rem_part!, rem_parts!, cascading_rem_part!, cascading_rem_parts!, gc!,
   copy_parts!, copy_parts_only!, disjoint_union, tables, pretty_tables,
-  @acset, constructor, PartsType, DenseParts, MarkAsDeleted, rem_free_vars!
+  @acset, constructor, undefined_subparts, PartsType, DenseParts, MarkAsDeleted, 
+  rem_free_vars!, parts_type
 
 using MLStyle: @match
 using StaticArrays: StaticArray
@@ -113,6 +114,15 @@ where X is the dom of the f in the schema
 """
 function dom_parts end
 
+"""
+Get the parts of the codomain of a morphism in an acset
+
+dom_parts(acs, f) == parts(acs, Y)
+
+where Y is the codom of the f in the schema
+"""
+function codom_parts end
+
 """
 Get the type assigned to a subpart in an acset, i.e.
 
@@ -391,6 +401,16 @@ Get a nullary callable which constructs an (empty) ACSet of the same type
 """
 function constructor end
 
+"""
+Given a hom, find which parts in its domain are undefined.
+"""
+function undefined_subparts end
+
+"""
+Get the type used to store parts IDs.
+"""
+parts_type(::ACSet{PT}) where {PT} = PT
+
 # Pretty printing
 #################
 
diff --git a/src/DenseACSets.jl b/src/DenseACSets.jl
index 5e7cc15..8488723 100644
--- a/src/DenseACSets.jl
+++ b/src/DenseACSets.jl
@@ -498,6 +498,14 @@ end
   parts(acs, @ct dom(s, f))
 end
 
+@inline ACSetInterface.codom_parts(acs::StructACSet{S}, f::Symbol) where {S} = _codom_parts(acs, Val{S}, Val{f})
+@inline ACSetInterface.codom_parts(acs::DynamicACSet, f::Symbol) = runtime(_codom_parts, acs, acs.schema, f)
+
+@ct_enable function _codom_parts(acs, @ct(S), @ct(f))
+  @ct s = Schema(S)
+  parts(acs, @ct codom(s, f))
+end
+
 @inline function ACSetInterface.incident(acs::SimpleACSet, part, f::Symbol)
   preimage(dom_parts(acs, f), acs.subparts[f], part)
 end 
@@ -644,6 +652,15 @@ end
 ACSetInterface.cascading_rem_parts!(acs::ACSet, type, parts) =
   delete_subobj!(acs, Dict(type=>parts))
 
+function ACSetInterface.undefined_subparts(acs::SimpleACSet{<:DenseParts}, f::Symbol)
+  findall([!haskey(acs.subparts[f],i) for i in dom_parts(acs,f)])
+end
+
+function ACSetInterface.undefined_subparts(acs::SimpleACSet{<:MarkAsDeleted}, f::Symbol)
+  codom_ids = codom_parts(acs,f)
+  findall([acs.subparts[f][i] ∉ codom_ids for i in dom_parts(acs,f)])
+end
+
 # Copy Parts
 ############
 
diff --git a/test/ACSets.jl b/test/ACSets.jl
index 9e0d581..18301e8 100644
--- a/test/ACSets.jl
+++ b/test/ACSets.jl
@@ -73,7 +73,10 @@ for dds_maker in dds_makers
   view(dds,:Φ) isa ColumnView
 
   # Deletion.
+  @test_throws ArgumentError undefined_subparts(dds, :X)
+  @test undefined_subparts(dds, :Φ) == []
   rem_part!(dds, :X, 2)
+  @test undefined_subparts(dds, :Φ) == [1]
   @test nparts(dds, :X) == 2
   @test incident(dds, 1, :Φ) == []
   if dds.parts[:X] isa IntParts
@@ -583,50 +586,74 @@ RecSch = BasicSchema(
   [],[]
 )
 
+# DenseParts
 @acset_type RecDataInj(RecSch, index=[:src,:tgt], unique_index=[:thing])
 @acset_type RecDataIdx(RecSch, index=[:src,:tgt,:thing])
 @acset_type RecDataNoIdx(RecSch)
 
-datainj = @acset RecDataInj begin
-    Thing=3
-    Node=3
-    Edge=3
-    thing=[1,2,3]
-    src=[1,1,2]
-    tgt=[1,2,3]
-end
-
-dataidx = @acset RecDataIdx begin
-  Thing=3
-  Node=3
-  Edge=3
-  thing=[1,2,3]
-  src=[1,1,2]
-  tgt=[1,2,3]
-end
+recdata_makers = [
+  RecDataInj,
+  RecDataIdx,
+  RecDataNoIdx,
+  () -> DynamicACSet("RecData", RecSch; index=[:src,:tgt]),
+  () -> AnonACSet(RecSch; index=[:src,:tgt])
+]
 
-datanoidx = @acset RecDataNoIdx begin
-  Thing=3
-  Node=3
-  Edge=3
-  thing=[1,2,3]
-  src=[1,1,2]
-  tgt=[1,2,3]
+for recdata in recdata_makers
+  mydata = recdata()
+  add_parts!(mydata, :Node, 3)
+  add_parts!(mydata, :Thing, 3, thing=[1,2,3])
+  add_parts!(mydata, :Edge, 3, src=[1,1,2], tgt=[1,2,3])
+
+  @test parts_type(mydata) <: DenseParts
+
+  new2old = cascading_rem_parts!(mydata, :Node, 1)
+
+  @test length(new2old[:Thing]) == nparts(mydata,:Thing)
+  @test nparts(mydata,:Thing) == 2
+  @test length(new2old[:Node]) == nparts(mydata,:Node)
+  @test nparts(mydata,:Node) == 2
+  @test length(new2old[:Edge]) == nparts(mydata,:Edge)
+  @test nparts(mydata,:Edge) == 1
+  @test incident(mydata, 3, :thing) == []
+  @test incident(mydata, 3, :src) == []
+  @test incident(mydata, 3, :tgt) == []
 end
 
-map_inj = cascading_rem_parts!(datainj, :Node, 1)
-map_idx = cascading_rem_parts!(dataidx, :Node, 1)
-map_noidx = cascading_rem_parts!(datanoidx, :Node, 1)
-
-@test map_inj == map_idx
-@test map_idx == map_noidx
+# MarkAsDeleted parts
+@acset_type RecDataInjMarkDel(RecSch, index=[:src,:tgt], unique_index=[:thing], part_type=BitSetParts)
+@acset_type RecDataIdxMarkDel(RecSch, index=[:src,:tgt,:thing], part_type=BitSetParts)
+@acset_type RecDataNoIdxMarkDel(RecSch, part_type=BitSetParts)
+
+recdata_makers = [
+  RecDataInjMarkDel,
+  RecDataIdxMarkDel,
+  RecDataNoIdxMarkDel,
+  () -> DynamicACSet("RecData", RecSch; index=[:src,:tgt], part_type=MarkAsDeleted),
+  () -> AnonACSet(RecSch; index=[:src,:tgt], part_type=MarkAsDeleted)
+]
 
-@test nparts(datainj,:Thing) == 2
-@test nparts(datainj,:Node) == 2
-@test nparts(datainj,:Edge) == 1
-@test incident(datainj, 3, :thing) == []
-@test incident(datainj, 3, :src) == []
-@test incident(datainj, 3, :tgt) == []
+for recdata in recdata_makers
+  mydata = recdata()
+  add_parts!(mydata, :Node, 3)
+  add_parts!(mydata, :Thing, 3, thing=[1,2,3])
+  add_parts!(mydata, :Edge, 3, src=[1,1,2], tgt=[1,2,3])
+
+  @test parts_type(mydata) <: MarkAsDeleted
+
+  new2old = cascading_rem_parts!(mydata, :Node, 1)
+
+  @test length(new2old[:Thing]) == nparts(mydata,:Thing)
+  @test nparts(mydata,:Thing) == 2
+  @test length(new2old[:Node]) == nparts(mydata,:Node)
+  @test nparts(mydata,:Node) == 2
+  @test length(new2old[:Edge]) == nparts(mydata,:Edge)
+  @test nparts(mydata,:Edge) == 1
+  # IDs are not updated in MarkAsDeleted, so "1" is the deleted element
+  @test incident(mydata, 1, :thing) == []
+  @test incident(mydata, 1, :src) == []
+  @test incident(mydata, 1, :tgt) == []
+end
 
 # attributes and an injective index
 RecAttrSch = BasicSchema(
@@ -648,9 +675,7 @@ dataattr = @acset RecAttrData{String,Symbol,Float64} begin
   attr3=[10.0,11.0,12.0]
 end
 
-map_attr = cascading_rem_parts!(dataattr, :Node, 1)
-
-@test map_inj == map_attr
+cascading_rem_parts!(dataattr, :Node, 1)
 
 @test all(map(x -> x ∈ subpart(dataattr,:attr1), ["2","3"]))
 @test only(subpart(dataattr,:attr2)) == :c