* Note: If you're using Chrome, you may have to install the Character Set Repairer extension to fix the charset and see the Japanese text. Sorry.
Welcome to this little shrine to Kyojuro Rengoku (alternatively, Rengoku Kyoujurou; and 煉獄杏寿郎 in Japanese characters) run by Møøse of Acidbrain. Kyojuro, or Rengoku-san as most of the other characters in Demon Slayer (Kimetsu no Yaiba. 鬼滅の刃) refer to him throughout the series, was an (unfortunately) short-lived, but hugely impactful character. He was the Flame Hashira (En Bashira, 炎柱), one of the highest-ranked members of the Demon Slayer Corps. He is also last in the long line of those taught Flame Breathing, beginning with his ancestor who had learned it from the various breathing forms' progenitor, Yoriichi Tsugikuni (Tsugikuni Yoriichi, 継国縁壱).
Rengoku-san's story remains mostly unchanged between the anime and the manga. In the manga, he first appeared in Chapter 44, Against Corps Rules (隊律違反), on January 17, 2017 in Weekly Shonen Jump issue 6, 2017. In the anime, his first appearance was in episode 21, which shared the same name and origionally aired in Japan on August 24, 2019. This is the beginning of the Rehabilitation Training Arc (Kinou Kaifuku Kunren-hen, 機能回復訓練編), but before Tanjiro Kamado (the main character, Kamado Tanjirou; 竈門炭治郎) and his friends can rehabilitate from their earlier exploits, Tanjiro must first meet the Hashira so they can decide his and his demon sister, Nezuko's (Kamado Nezuko, 竈門禰󠄀豆子), fates. Though he was a bit harsh, Rengoku-san was merely sticking strictly to the rules as one doing his duty as a Hashira should.
Now we get to talk about the creme of the crop, the Mugen Train Arc (Mugen Ressha-hen, 無限列車編). This is Rengoku-san's center stage. It was first released as a movie on October 16, 2020 in Japan. Tanjiro, Nezuko, and their two friends, Zenitsu Agatsuma (Agatsuma Zenitsu, 我妻善逸) and Inosuke Hashibira (Hashibira Inosuke, 嘴平伊之助) are told by Insect Hashira (Mushi Bashira, 蟲柱) Shinobu Kocho (Kochou Shinobu, 胡蝶しのぶ) to meet up with Rengoku-san on the Infinity Train (Mugen Ressha, 無限列車) as there have been some suspected demon activity. I won't spoil it all for you, but they end up meeting Enmu (魘夢), Lower Rank One (Kagen no Ichi, 下弦の壱), resulting in a pretty epic fight, but after the Demon Slayers win against Enmu, the movie culminates in a fight-to-the-death against the Flame Hashira and the extremely powerful Upper Rank Three (Jogen no San, 上弦の参), Akaza (猗窩座). Akaza is a demon with power unlike any the Demon Slayer Corps have ever met before. Rengoku-san ends up passing away due to his injuries in a bitersweet ending.
The Mugen Train Arc returned to TV on October 10, 2021 in Japan with an extra episode to honor Rengoku-san, Flame Hashira Kyojuro Rengoku (En Bashira Rengoku Kyoujurou, 炎柱・煉獄杏寿郎). But other than this, well, basically filler episode but cute insight into how Rengoku-san works as a Hashira, not much else is changed except maybe some small added inserts and graphic updates.
However, gone, he was not forgotten. Rengoku-san left a huge impact on Tanjiro, and gave him the will to fight. After Tanjiro's sword was broken for the 8666938478347th time, he adopted Rengoku-san's hilt (tsuba, 鍔) as his own. He even remembered Rengoku-san's words to him as he tried to pep-talk another member, Water Hashira (Mizu Bashira, 水柱) Giyu Tomioka (Tomioka Giyuu, 冨岡義勇).
Rengoku-san was a strong man with resolve, parted to him by his dying mother, Ruka (Rengoku Ruka, 煉獄瑠火) when he was but a child. And in a way also by his drunkard father, the former Flame Hashira (as the title was passed down through their family), who just gave up on both himself and Kyojuro, further giving the stubborn Hashira more reason to continue. Rengoku-san thought those without talent (surely an after-effect of dealing with his father) could do whatever they wanted if they just tried hard enough. But, Rengoku-san, we know you were talented: after all, you taught yourself Flame Breathing and became a Hashira just by reading three manuscripts—the rest having been torn up by Shinjuro (Rengoku Shinjurou, 煉獄槇寿郎).
And I guess no Rengoku-san shrine could be complete without the mention of Senjuro, (Rengoku Senjurou, 煉獄千寿郎), the little brother Kyojuro had to raise and wanted to help protect even at the cost of his own life. A little known fact, as a bonus, is that Love Hashira (Koi Bashira, 恋柱) Mitsuri Kanroji (Kanroji Mitsuri, 甘露寺蜜璃) was his supposed-to-be successor (tsukugo, 継子) and she and Senjuro both introduced him to his favorite snack, sweet potatoes, during a workout session one day.