Exploring Time
After landing, Kate explores the fictional MHA Anime Universe. By looking for Izuku Midoriya who was the protagonist, but she will learn not everything is the same as the Anime.
Disclaimers: I own nothing
Kate Kane/Batwoman's POV
"Last time, I thought my life was over when the plane I was onboard in crashed, but then suddenly I found myself in some void and some person with a Metallic Voice tells me I will be reborn in some Universe where it's actually a fictional Anime. I wonder what Anime that was fictional I will be landing in, if I'm there then that will probably mean I'm stuck there permanently."
"Anyway here goes nothing."
End of POV
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Present Time
When Kate wakes up and finds herself in a Batcave that looks really identical to the one in Wayne Tower, it's just a little expanded. She sees the 2 Batmobiles which is the ones she knows but the second she doesn't recognize at all, she see a Batwing and a Batboat, plus her familiar Batbike is there too. She sees her Batsuit which is the same one she modified with Red Colors and the Red Wig she's been using through her days on saving Gotham from Crime after Bruce was absent, all of her Bat Tools and Equipment are there too. Lastly there is the same Bat Computer she will need as well.
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"Let's see where I am", Kate gets the Bat Computer working to pinpoint her location or where the Batcave is.
What Kate learn is the Batcave is located outside the Big City much to her surprise is identified as Musutafu City, "Am I in the Fictional Anime known as the My Hero Academy? Well I should find out for myself rather than looking at Bat Computer and see if I can find the protagonist of MHA who's name is Izuku Midoriya, but I'll be using the Batwing this time, I think know how to fly it for sure", Kate puts on her Batwoman Costume then boards the Batwing and then flies out the Batcave to see for herself and look for Izuku Midoriya.
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"Oh this Batwing has a stealth mode and VTOL mode, interesting. This might help me look for Izuku Midoriya undetected", Batwoman activates the stealth on the Batwing so she won't be detected on radar while she looks for Izuku.
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Musutafu City, High above
"Activating VTOL mode", Batwoman activates the Batwing's VTOL mode and use it's video camera to search for Izuku Midoriya who could be anywhere in the city.
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"Izuku Midoriya began as Quirkless or just powerless, until he met his idol Toshinori Yagi AKA All Might who was the Symbol of Peace but have seen his weaken form that he sustain from his battle against his arch-nemesis All For One. Izuku had a Quirk which he was sharing with All Might after he made him his apprentice", Batwoman talked about what she knows about the MHA Anime but focus on Izuku's rise to a Hero that he wanted to be.
Anyway Batwoman continues looking for Izuku high above the city and eventually he catches a glimpse of Izuku walking with a woman holding hands with him, "Yu Takeyama AKA Mt Lady, Quirk Gigantification. What is she his lover? Because, I'm pretty sure they had no relationship in the actually MHA Anime, unless this is an alternate MHA Universe that I landed in.
Batwoman zooms the camera closer and scans Izuku for his Quirk and it turns out he has the One For All Quirk, "that's good news, well that's all I came to see and now I will go back to the Batcave", just like that, Batwoman flies back to the Batcave.
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Batcave
Batwoman is checking the Batcomputer again to see what should she do next and she has answer to that. "I will be paying UA High a visit", that's her plan all right.
End
After learning that she is the Musutafu City of the MHA Anime Universe and learning what she can, Kate decided to pay a visit to the school that is used to train Students to become a next generation of Super Quirk Heroes which is UA High.
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Notes: Oh Reagan was a love interest for Kate but they break up twice, Reagan said in the end that she is hooked with some British Woman. In this Fanfic, Kate's and Reagan's relationship will be restarted now Reagan is stuck with Kate in the MHA Universe. Right now she won't be encounter at the moment for the next chapters.
Notes 2: Even though I'm using the Batwing/Batplane that appears in Batman Forever Film, In this fanfic it has the same VTOL Mode much like the Bat in the Dark Knight Rises Film and has stealth abilities. It also has Missiles and MG as weapons.
Notes 3: I say in this fanfic, Kate has already seen the MHA Anime which would explain how she knows about it.
Notes 4: While Kate was speaking to Earth-99 Bruce Wayne during the Crisis on Infinite Earth, there was a Batmobile seen in the Batcave but it was covered in sheets. According to Arrowverse Wikia, it looks like the Batmobile seen in the 1989 Batman and Batman Returns Films.