Nekomata.

Alternative Name: ねこまた。
Author: Kuku Hayate
Artist: Kuku Hayate
Category: Manga, Fantasy, Historical, Seinen, Supernatural
Reading Direction: Right to Left
Status: Ongoing
Translator(s)/Scanlation Group: INP-Mangaz
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Description:
The setting is Edo–…the imperial capital.  Protecting the streets is Jinbē, the “Mumbling Chief,” and a police officer.  He’s a reliable man whose only flaw is that he talks to himself a lot.  However, he has a secret reason for that…  A story about these cute “nekomata,” Jinbē’s home, empathy, and cuteness begins!