diff --git a/src/categorical_algebra/HomSearch.jl b/src/categorical_algebra/HomSearch.jl
index ef1a4d7d5..3c20e91fa 100644
--- a/src/categorical_algebra/HomSearch.jl
+++ b/src/categorical_algebra/HomSearch.jl
@@ -589,7 +589,18 @@ function Base.iterate(Sub::SubobjectIterator, state=SubobjectIteratorState())
   for o in ob(S)
     for p in parts(dX, o)
       rem = copy(dX)
-      comps = delete_subobj!(rem, Dict([o => [p]]))
+      comps = Dict{Symbol, Any}(pairs(delete_subobj!(rem, Dict([o => [p]]))))
+      rem_free_vars!(rem)
+      for at in attrtypes(S)
+        comps[at] = map(AttrVar.(parts(rem, at))) do part
+          for (f, c, _) in attrs(S; to=at)
+            inc = incident(rem, part, f)
+            if !isempty(inc)
+              return dX[comps[c][first(inc)], f]
+            end
+          end
+        end
+      end
       h = ACSetTransformation(rem, dX; comps...) ⋅ X
       if !is_seen(state, h)
         push!(state, h)
diff --git a/test/categorical_algebra/HomSearch.jl b/test/categorical_algebra/HomSearch.jl
index 69288eb7f..a62da793e 100644
--- a/test/categorical_algebra/HomSearch.jl
+++ b/test/categorical_algebra/HomSearch.jl
@@ -156,16 +156,24 @@ end
 ###########################
 
 G = path_graph(Graph, 3)
-subG, subobjs = subobject_graph(G) |> collect
+subG, subobjs = subobject_graph(G)
 @test length(subobjs) == 13 # ⊤,2x •→• •,2x •→•, •••,3x ••, 3x •, ⊥
 @test length(incident(subG, 13, :src)) == 13 # ⊥ is initial
 @test length(incident(subG, 1, :src)) == 1 # ⊤ is terminal
 
+# With attributes
+G′ = path_graph(WeightedGraph{Bool}, 3)
+G′[:weight] = [false, AttrVar(add_part!(G′, :Weight))]
+subG′, subobjs′ = subobject_graph(G′)
+@test is_isomorphic(subG, subG′)
+@test nparts(dom(hom(first(subobjs′))), :Weight) == 1
+@test nparts(dom(hom(last(subobjs′))), :Weight) == 0
+
 # Graph and ReflexiveGraph should have same subobject structure
-subG, _ = subobject_graph(path_graph(Graph, 2))
-subRG, sos = subobject_graph(path_graph(ReflexiveGraph, 2))
+subG2, _ = subobject_graph(path_graph(Graph, 2))
+subRG2, sos = subobject_graph(path_graph(ReflexiveGraph, 2))
 @test all(is_natural, hom.(sos))
-@test is_isomorphic(subG, subRG)
+@test is_isomorphic(subG2, subRG2)
 
 # Partial overlaps 
 G, H = path_graph.(Graph, 2:3)