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. Plus somethings that's she suppose to use as Batwoman looks unfamiliar and different including the Batcave.
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 back in my Earth. 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 except looks more vast than the original, "it's just looks a little expanded or vast", Kate said seeing some extra space around the Batcave. She sees the 2 Batmobiles which is the one she knows but the second she doesn't recognize at all, she see a Batwing and a Batboat which she doesn't recognize ether, 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 from being Batman, all of her Bat Tools and Equipment are there too. Lastly there is the same Bat Computer she will need as well. Also she 3 other vehicles she doesn't recognize from her Earth, 2 are mechs that have signs of them and reads Knightcrawler and Justice Buster, lastly the last one is aircraft called the Flying Fox.
"Some of these Vehicles I don't recognize such as the Batwing, Batboat, Tumbler, Knightcrawler, Justice Buster and Flying Fox, but still they could be useful from where I am now", Kate said after inspecting and talking a good look at all of the Vehicles that are all new to her.
"All my Bat-Tools are all here, plus it seems I also have all of the materials I need to make an endless supply of the tools I need whenever I go out as Batwoman, also I have the Railgun that Tommy Elliot stole from Wayne Enterprises" Kate said after seeing everything she needs even the Railgun that Tommy was going to use to kill Batman before only to be thwarted by Batwoman.
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"Let's see where I am", Kate then gets on the Bat-Computer and 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 and goes by Hero alias Deku, but I'll be using the Batwing this time, I think know how to fly it for sure, even though this new to me", Kate puts on her Batwoman Costume then boards the Batwing and then flies out the Batcave without any problem to see for herself and look for Izuku Midoriya.
"For some reason I seem to have no problem on knowing how to fly the Batwing."
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"Oh this Batwing has a stealth mode and VTOL mode, interesting. This might help me look for Izuku Midoriya undetected by anyone's radar", Batwoman activates the stealth mode on the Batwing so she won't be detected on radar while she looks for Izuku.
"I did watch MHA Anime during most of my time and gain some knowledge about the Anime, unlike my Earth, every Hero are working for the Governments and the UN because the maker of MHA never put the part where the MHA Cast are suppose to also battle Corrupt Officials. But still even though I'm here I no there is corruption here too", Batwoman to said to herself about what she knows of the MHA Universe even the fact there is corruption too, it's just doesn't shows itself.
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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 doing whatever he is doing.
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"Izuku Midoriya began and started of as Quirkless or just powerless which left him sadden when he realize he cannot fulfill his dream, 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 right after meeting All Might.
"Priors before that, Izuku had a fallout with his friend Katsuki Bakugo after learning he was Quirkless and started to bully him while he had an Explosion Quirk. Despite Izuku is sharing All Might his Quirk and being student in UA High, Katsuki still wants to prove that he is better than Izuku."
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Anyway Batwoman continues looking for Izuku high above the city and eventually he catches a glimpse of Izuku walking with a familiar 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 where they are lovers."
"Mt Lady and Izuku rarely interreacted with each other in the actually MHA Anime which is Canon since all they is all Team up with Heroes against Villains."
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. But she will be going to UA as Batwoman too.
"Also I'll keep myself undetected by anyone because in MHA Universe which is a Alternate Universe, I'm a total stranger who doesn't have Quirk and just my Military Training to fight crime."
End
After learning that she is the Musutafu City of the MHA Anime Universe which isn't the same like the Canon 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 and see what else is different from the Canon.
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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 after her Final Betrayal. 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 a white sheets. According to Arrowverse Wikia, it looks like the Batmobile seen in the 1989 Batman and Batman Returns Films.