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Classical definitions of weak higher-dimensional categories are given inductively, for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent definitions of weak n-categories for all natural numbers n, or of weak $\omega$ -categories, take more sophisticated approaches, and the nature of the ‘hom is often not immediate from the definitions’. In this paper, we focus on Leinster’s definition of weak $\omega$ -category based on an earlier definition by Batanin and construct, for each weak $\omega$ -category $\mathcal{A}$ , an underlying (weak $\omega$ -category)-enriched graph consisting of the same objects and for each pair of objects x and y, a hom weak $\omega$ -category $\mathcal{A}(x,y)$ . We also show that our construction is functorial with respect to weak $\omega$ -functors introduced by Garner.

Aspergillosis is a rare disease that often occurs in patients with diabetes mellitus or compromised hosts. This study describes a 60-years-old woman with unusual pseudo-malignant paranasal invasive aspergillosis with 18F-fluorodeoxyglucose (18F-FDG) uptake treated by endoscopic sinus surgery. To the best of our knowledge, there are few reported cases of paranasal fungal infection with 18F-FDG uptake.A 60-years-old woman was presented with headache and nasal obstruction.Computed tomography (CT) showed a shadow with bone destruction in the sinus cavity and accumulation of 18F-FDG uptake. The patient was diagnosed with a malignant tumor or pseudo-malignant paranasal invasive aspergillosis.The patient underwent endoscopic sinus surgery; no neoplastic lesions were detected in the areas with CT shadows. All the observed fungal mass reservoirs were removed.The patient remained hospitalized for 1 week after the surgery with no significant postoperative abnormalities. There was no recurrence of the disease for 6 months, and the patient's symptoms resolved, indicating a good course of follow-up.Invasive aspergillosis should be considered a differential disease when positron emission tomography (PET)/CT scans show FDG uptake, CT shows bone destruction, and T2-weighted MRI scans show a low signal.

Eosinophilic chronic rhinosinusitis (ECRS) is a Type 2 inflammatory disease that manifests as chronic inflammation of the paranasal sinus. IL-4/IL-13 receptor monoclonal antibodies (dupilumab) to suppress Type 2 inflammation have become a good treatment option for patients who are refractory to surgery. Most patients respond normally, although significant side effects such as eosinophilic pneumonia may occur, requiring discontinuation of dupilumab. Here, we present a case in which dupilumab administration caused a side-effect of eosinophilic pneumonia. A 65-year-old woman presented with nasal obstruction and olfactory dysfunction due to a nasal polyp. Her symptoms temporarily improved with dupilumab; however, dupilumab was discontinued due to eosinophilic pneumonia. Discontinuation of dupilumab resulted in the rapid resolution of eosinophilic pneumonia and reappearance of nasal polyps. We, therefore, resumed dupilumab treatment in combination with low-dose steroids; eosinophilic pneumonia did not flare up, and the nasal polyps shrank steadily. There is no established treatment strategy in cases where a side effect of eosinophilic pneumonia arises while treating ECRS with dupilumab. Based on the described case, we recommend that a combination of a low-dose steroids and dupilumab be considered as a treatment option to counter the side-effect of eosinophilic pneumonia induced by dupilumab alone.