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libraryofgage · 1 year ago

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A Place Like Steve in a Boy Like This (2)

Part of: Steve Deserves Good Parents, Actually Debbie and Fester Addams One | Two | Three Rick and Evelyn O'Connell One | Two (you're here!) Harley Quinn One 10th Doctor and Rose One | Two (on the way!) Scooby Gang (there are plans for this one lmao, so plz be patient with me orz) Jedidiah and Octavius (from Night at the Museum) (I also have plans for this one actually they just need to simmer a little lmao)

Hi welcome back to my Mummy Crossover where Steve's parents are Rick and Evelyn O'Connell this took forever bcuz the words didn't want to word correctly lmao

Anyway, here we are! Some interactions, some more insight on all of Steve's talents, a teensy bit of chaos killed before it could flourish. What more could you want?

As always, if you see any typos, no you didn't ;)

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"Breathe in."

Steve slowly inhales, keeping his chest and arms steady.

"Now pull as you breathe out."

Steve steadily exhales, squeezing the trigger as he does, and feeling the gun kick in his hand. Several yards away, a tin can that's little more than a speck in the distance topples to the ground.

Before Steve can realize his aim was good, the gun is plucked from his hand and he's lifted into the air. Weightlessness overwhelms him, and he shrieks with delight as he falls back into his father's arms. "That's my boy!" his father says, tossing him into the air again.

"Oh, do be careful, Rick. He broke an arm the last time you threw him around like that," Steve's mother says, a proud smile tugging at her lips despite her words.

Steve finds himself safely held in his father's arms a second later, his heart racing and his breaths short from exhilaration. "Again! Again!" he shouts, looking up at his father hopefully.

"Sorry, kiddo, you heard your mother," his father says, messing up Steve's hair before lifting him onto his shoulders. Steve grips his father's hair tightly, grinning as his father jogs over to the tin can. "You'll be able to shoot running in no time."

"Am I gonna be as good as you?" Steve asks, leaning over his father's head. "How long will that take?"

"You'll be better than me, Steve. It'll take a few years, though. At least one hundred."

"One hundred?! I'm gonna be bones by then! Dust and bones!"

"Nah, you'll be fine," his father says, waving his hand dismissively.

"I'll be dead!"

"In my experience, the dead don't make a habit of staying that way."

Steve huffs and rolls his eyes, pinching his father's cheeks and tugging on them until he laughs, grabs Steve's hand, and playfully bites his fingers. Steve shrieks again, laughing as he tugs his hand away and yanks on a few strands of his father's hair for revenge.

------

Steve, Max, and Eddie get discharged within days of each other, and even though Steve was expecting his house to be invaded by his friends, he still finds himself wishing he'd had a few more days with his parents before everyone showed up and started interrogating him. In fact, he almost considers ignoring the doorbell when it rings the day after Max is discharged.

"Steve!" Rick shouts, his voice carrying all the way from his carefully maintained weapons room. "Can you get that?"

"Can't put it off any longer," Robin says, grinning at him from her spot on the couch. She stretches out her leg and nudges Steve's thigh, urging him to get up.

He sighs, pushing himself off the couch and grimacing at the slight tug on his sides. "Got it," he calls back, walking to the door and bracing himself before opening it.

The porch is packed with his friends, Dustin and Eddie at the very front. "Finally!" Dustin says, pushing past Steve to get into the house.

Everyone else streams in after him, and Steve ends up just holding the door. "Yeah, welcome in, make yourselves at home, thanks so much for calling before showing up," he mutters, closing the door after the final person, Will, has walked inside.

He follows after them, relieved they filter into the living room instead of heading to the kitchen. Uncle Jonathan has been in there all day, trying his hand at a new gin brewing technique that makes Steve's head spin just thinking about it.

Steve flops onto the couch next to Robin, dropping his head onto her shoulder. Dustin looks ready to speak, and Steve is ready to pretend he's listening, when his mother walks into the room. She looks around with a concerned frown, her fingers covering her mouth and tapping against her lips. "Steve," she says, her voice slightly distracted, "dónde está el machete de tu papá?"

"En el garaje," he replies, waving off her thanks.

"You speak Spanish?" Max asks, glancing at Evelyn as she walks past her to reach the garage.

"I speak several languages," Steve tells her. He feels the couch shift next to him and looks over to see Will scooting over to make room for Eddie. "Spanish, Hebrew, Arabic, Egyptian, French, Greek, a little Urdu, but that one is rusty."

"Holy shit," Mike says, staring at Steve like he's shapeshifted into an alien, "you're smart?!"

"Wait, is that how you guys cracked the Russian code so quickly?" Dustin asks. "Why did you make Robin learn Russian if you already knew it?"

"I didn't make Robin do anything. She started learning while I called a guy I know who can speak Russian. He only managed to get back to me the same day Robin got the whole thing translated."

"You know a guy who can speak Russian?" Eddie asks, raising an eyebrow at Steve when he glances over.

Steve shrugs. "I know a lot of guys who know a lot of things. I met all of them while traveling with my parents," he explains.

"Where have you been?" Will asks.

"Every continent except Antarctica. More places than I can count, actually."

"Why did you travel so much?" El asks, her gaze drifting toward the mantle where several of his mother's souvenirs are carefully arranged. "Did those come from your travels?"

"I followed my parents while they worked until high school. And yeah, those are souvenirs, you can pick them up, but be careful."

As though the lack of permission was the only thing holding her back, Max jumps up and hurries over to the mantle, pulling down a small jar and turning it over in her hands. Its lid is shaped like the head of Anubis, and Steve is just realizing what she's picked up when his father walks into the room.

Rick stops, stares at the jar in Max's hand, and then marches over to her, a man on a mission. He swipes the jar, ignoring Max's shout in protest, and looks it over carefully. His expression becomes disbelieving, fond, and annoyed all at once. "Evie!" he shouts, turning around and about to go looking for her when she appears in the doorway.

"No need to shout, dear, I was just in the other room," she says, smiling until she sees the jar he's holding.

Her expression says it all, but Rick still holds the jar up, smiles sweetly at her, and asks lightly, "Evie, darling, is this what I think it is?"

"Well," Evelyn says, rolling her shoulders back in a way that tells Steve they're about to argue. And then start kissing like nobody's around. "It very well might be."

"What is it?" Dustin asks, sliding closer to get a better look at the jar when Rick holds it higher.

"Really, Evie? Did you forget the part where these things are cursed? Did you completely forget what happened to the Americans who touched these?"

"Aren't you American?" Max asks.

"And aren't you touching it?" Erica adds.

"It's certainly not cursed anymore," Evelyn says, walking over and easily plucking the jar from Rick's hands. She looks it over, idly brushing off some of the dust. "Imhotep is thoroughly dead. You made sure of that, dear."

"I'm sorry, did she say cursed?" Mike asks.

"Yes," El says.

As Evelyn and Rick stare each other down, Steve sighs and drops his head on the back of the couch. "It's a jar used in ancient Egypt to store the organs of mummies. That one specifically belonged to Imhotep, a mummy with a curse. He ate people and tried to sacrifice my mom to bring his girlfriend back and killed a bunch of Americans in the process. But Mom and Dad defeated him, like, twice and he hasn't been a problem since, so Mom is pretty sure he's gone for good now."

"There is no way any of that is true," Max says, huffing as Rick takes the jar back before Evelyn can even think of letting Max look at it again. "I mean, seriously? Mummies?"

"Oh, inter-dimensional monsters are perfectly believable, but mummies are a step too far?" Steve asks.

"Inter-dimensional monsters?" Evelyn asks, whirling around on Steve and placing her hands on her hips.

"So that's where he gets it from," Eddie says, his voice soft and more than a little amused.

Before Steve can comment on that (or try to kick Eddie from where he's sitting on the couch), his father moves to stand next to his mother, arms crossed over his chest with a stern look and still holding the jar. "Wanna share with the class, kid?" he asks.

Steve grimaces, knowing that tone of voice and sinking a little lower on the couch. "Not really, no. Most of the class is already in the loop."

"Humor us," his mother says, her voice firm and leaving no room for argument.

"Gee," Erica says, shifting closer to the doorway, "I'm suddenly feeling pretty hungry. Anyone else wanna go loot the kitchen?"

"I'm in," Max says, hurrying across the room in long strides.

"So are we," Mike adds, grabbing Will's hand and dragging him along before he can get caught up in whatever shit storm might occur. Lucas quickly follows after, flashing an apologetic smile at Steve once he's behind Evelyn and Rick.

They've all disappeared before Steve can warn them about Jonathan's gin experiments, but he figures they deserve to have their nostrils burned from the smell for abandoning him.

Only Steve, Robin, Eddie, Dustin, and El are left with Steve's parents frowning and looking at them expectantly. Steve manages to hold out under their stare for a few seconds before he sighs, sits up straight, and waves for them to sit in the loveseat perpendicular to the couch.

Once they're settled, he glances at Dustin, gets a shrug in return, and rolls his eyes. Robin places a hand on his shoulder, getting his attention to flash a grin and say, "Good luck, dingus. Just know I'll be thoroughly entertained by the end of this."

"Gee. Thanks."

Eddie snorts, settles back into the couch, and helpfully offers, "I mean, it can't be worse than being the main course of a demobat feast, right?"

"Oh, I assure you," Evelyn says, her eyes narrowing, "it certainly can."

"Oh, damn," Eddie says, shaking his head, "What do you want on your tombstone, Stevie?"

Steve rolls his eyes as Robin laughs and high-fives Eddie. He ignores them for now, secretly grateful for the lighter feeling in his chest that their joking has given him, and looks at his parents. "I guess it started with Will's disappearance."

-------

Tag List (there should be room still! So, if you'd like a tag, let me know!)

@trueghostqueen, @swimmingbirdrunningrock, @thoughtfulbreadpolice, @mogami13, @blcksh33p1987, @beawritingbooks, @remus-is-trans, @your-confused-friend, @estrellami-1, @nburkhardt, @vacantwatchers, @yeahhhh-suga, @phantomcat94

@blackpanzy, @ape31, @croatoan-like-its-hot, @plantzzsandpencilzzs, @flustratedcas, @anne-bennett-cosplayer, @just-a-tiny-void, @disrespectedgoatman, @fallingleavesinthewind, @nymime, @nectandra, @moomkin77, @nadenia, @resident-disappointment, @copper-arrows, @romanticdestruction, @rowanshadow26

#steddie #steddie fic #steve harrington #eddie munson #the mummy 1999 crossover #rick o'connell #evelyn o'connell #jonathan carnahan #steve deserves good parents actually #i'm realizing i always post these late at night lmao #work really do be having me writing late orz #anyway i battled valiantly and still got defeated by some of the tags on this list i'm #i just don't know why some of them don't link properly :/

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bubbloquacious · 4 months ago

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Okay so to get the additive group of integers we just take the free (abelian) group on one generator. Perfectly natural. But given this group, how do we get the multiplication operation that makes it into the ring of integers, without just defining it to be what we already know the answer should be? Actually, we can leverage the fact that the underlying group is free on one generator.

So if you have two abelian groups A,B, then the set of group homorphisms A -> B can be equipped with the structure of an abelian group. If the values of homorphisms f and g at a group element a are f(a) and g(a), then the value of f + g at a is f(a) + g(a). Note that for this sum function to be a homomorphism in general, you do need B to be abelian. This abelian group structure is natural in the sense that Hom(A ⊗ B,C) is isomorphic in a natural way to Hom(A,Hom(B,C)) for all abelian groups A,B,C, where ⊗ denotes the tensor product of abelian groups. In jargon, this says that these constructions make the category of abelian groups into a monoidal closed category.

In particular, the set End(A) = Hom(A,A) of endomorphisms of A is itself an abelian group. What's more, we get an entirely new operation on End(A) for free: function composition! For f,g: A -> A, define f ∘ g to map a onto f(g(a)). Because the elements of End(A) are group homorphisms, we can derive a few identities that relate its addition to composition. If f,g,h are endomorphisms, then for all a in A we have [f ∘ (g + h)](a) = f(g(a) + h(a)) = f(g(a)) + f(h(a)) = [(f ∘ g) + (f ∘ h)](a), so f ∘ (g + h) = (f ∘ g) + (f ∘ h). In other words, composition distributes over addition on the left. We can similarly show that it distributes on the right. Because composition is associative and the identity function A -> A is always a homomorphism, we find that we have equipped End(A) with the structure of a unital ring.

Here's the punchline: because ℤ is the free group on one generator, a group homomorphism out of ℤ is completely determined by where it maps the generator 1, and every choice of image of 1 gives you a homomorphism. This means that we can identify the elements of ℤ with those of End(ℤ) bijectively; a non-negative number n corresponds to the endomorphism [n]: ℤ -> ℤ that maps k onto k added to itself n times, and a negative number n gives the endomorphism [n] that maps k onto -k added together -n times. Going from endomorphisms to integers is even simpler: evaluate the endomorphism at 1. Note that because (f + g)(1) = f(1) + g(1), this bijection is actually an isomorphism of abelian groups

This means that we can transfer the multiplication (i.e. composition) on End(ℤ) to ℤ. What's this ring structure on ℤ? Well if you have the endomorphism that maps 1 onto 2, and you then compose it with the one that maps 1 onto 3, then the resulting endomorphism maps 1 onto 2 added together 3 times, which among other names is known as 6. The multiplication is exactly the standard multiplication on ℤ!

A lot of things had to line up for this to work. For instance, the pointwise sum of endomorphisms needs to be itself an endomorphism. This is why we can't play the same game again; the free commutative ring on one generator is the integer polynomial ring ℤ[X], and indeed the set of ring endomorphisms ℤ[X] -> ℤ[X] correspond naturally to elements of ℤ[X], but because the pointwise product of ring endomorphisms does not generally respect addition, the pointwise operations do not equip End(ℤ[X]) with a ring structure (and in fact, no ring structure on Hom(R,S) can make the category of commutative rings monoidal closed for the tensor product of rings (this is because the monoidal unit is initial)). We can relax the rules slightly, though.

Who says we need the multiplication (or addition, for that matter) on End(ℤ[X])? We still have the bijection ℤ[X] ↔ End(ℤ[X]), so we can just give ℤ[X] the composition operation by transfering along the correspondence anyway. If p and q are polynomials in ℤ[X], then p ∘ q is the polynomial you get by substituting q for every instance of X in p. By construction, this satisfies (p + q) ∘ r = (p ∘ r) + (q ∘ r) and (p × q) ∘ r = (p ∘ r) × (q ∘ r), but we no longer have left-distributivity. Furthermore, composition is associative and the monomial X serves as its unit element. The resulting structure is an example of a composition ring!

The composition rings, like the commutative unital rings, and the abelian groups, form an equational class of algebraic structures, so they too have free objects. For sanity's sake, let's restrict ourselves to composition rings whose multiplication is commutative and unital, and whose composition is unital as well. Let C be the free composition ring with these restrictions on one generator. The elements of this ring will look like polynomials with integers coefficients, but with expressions in terms of X and a new indeterminate g (thought of as an 'unexpandable' polynomial), with various possible arrangements of multiplication, summation, and composition. It's a weird complicated object!

But again, the set of composition ring endomorphisms C -> C (that is, ring endomorphisms which respect composition) will have a bijective correspondence with elements of C, and we can transfer the composition operation to C. This gets us a fourth operation on C, which is associative with unit element g, and which distributes on the right over addition, multiplication, and composition.

This continues: every time you have a new equational class of algebraic structures with two extra operations (one binary operation for the new composition and one constant, i.e. a nullary operation, for the new unit element), and a new distributivity identity for every previous operation, as well as a unit identity and an associativity identity. We thus have an increasing countably infinite tower of algebraic structures.

Actually, taking the union of all of these equational classes still gives you an equational class, with countably infinitely many operations. This too has a free object on one generator, which has an endomorphism algebra, which is an object of a larger equational class of algebras, and so on. In this way, starting from any equational class, we construct a transfinite tower of algebraic structures indexed by the ordinal numbers with a truly senseless amount of associative unital operations, each of which distributes on the right over every previous operation.

#math #the ongoing effort of valiantly constructing complicated mathematical structures with 0 applications #i know i owe you guys that paraconsistency effortpost still #it's coming! just hard to articulate so far #so if you start with the equational class with empty signature your algebras are just sets #the first iteration of the construction gets you the class of monoids #but after that it's what i guess you could call 'near-semirings'?

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