chain morphism between subdivisions

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I am trying to compute a morphism between chain complexes (and homology/cohomology ultimately) that is induced by a simplicial map. The problem seems to be when I try to specify the map between barycentric subdivisions.

As a concrete example - this works:

S = SimplicialComplex([[1,2]],is_mutable=False)
T = SimplicialComplex([[1,2],[2,3],[1,3]],is_mutable=False)
f = {x[0]:x[0] for x in S.cells()[0]}
H  = Hom(S,T)
z = H(f)
r = z.associated_chain_complex_morphism()

If I try to do the same with the subdivision - I get

S = SimplicialComplex([[1,2]],is_mutable=False).barycentric_subdivision()
S.set_immutable()
T = SimplicialComplex([[1,2],[2,3],[1,3]],is_mutable=False).barycentric_subdivision()
T.set_immutable()
f = {x[0]:x[0] for x in S.cells()[0]}
H  = Hom(S,T)
z = H(f)
r = z.associated_chain_complex_morphism()

I get:

ValueError: matrices must define a chain complex morphism

Any insight would be helpful.