hierarchical model

[Kaxzert]

hello everybody!
i have a few problem with exercise 5 in chapter 3
exercise 5 build hierarchical model using cat dimension. So i want to build a hierarchical model where i have distribution for each cat and using each cat distribution determine distribution for each aa. I did look up what the author have done with this exercise. Although the author did not use this kind of structure. But i want to test around with this
this is my code:

diff = chem_data.theo - chem_data.exp

cat_encode = pd.Categorical(chem_data['cat'])
idx_cat = cat_encode.codes

aa_encode = pd.Categorical(chem_data['aa'])
idx_aa = aa_encode.codes

coords = {"cat": cat_encode.categories, "aa":aa_encode.categories}

with pm.Model(coords=coords) as cs_hh:
    #hyper
    µ_mu = pm.Normal('µ_mu', mu=0, sigma=10)
    µ_std = pm.HalfNormal('µ_std', sigma=10)
    σ_std = pm.HalfNormal('σ_std', sigma=10)
    #parameter for cat
    μ_cat = pm.Normal('μ_cat', mu=µ_mu, sigma=µ_std, dims="cat")
    σ_cat = pm.HalfNormal('σ_cat', sigma=σ_std, dims="cat")
    #paremater for aa
    µ = pm.Normal('µ', mu=μ_cat[idx_cat], sigma=σ_cat[idx_cat], dims='aa')
    σ = pm.HalfNormal('σ', sigma=10, dims='aa')

    y = pm.Normal('y', mu=µ[idx_aa], sigma=σ[idx_aa], observed=diff)
    idata_cs_hh = pm.sample()

the error arises where dims of µ can not shape from shape(1776,) to shape(19,) i do not know why µ for aa is in shape of (1776,). I am new to probability language like pymc and i still dont really understand much about the structure in pymc model. Forgive me if this is a silly question.

thank for your help!