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Category Theory Notation Cheat Sheet

Symbol	Meaning	Example	Notes
\mathcal{C}, \mathcal{D}, \mathcal{E}	Categories	$$\mathcal{A}, \mathcal{B}, \mathcal{C}$$	Calligraphic uppercase letters for categories. Multi-letter names allowed. In LaTeX, use 'calrsfs' package for better multi-letters.
A, B, X, Y	Objects	$$A, B, A_\mathcal{C}, B_\mathcal{B}$$	Plain uppercase letters. Subscripts indicate which

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Vector Operations & Operators

• Vectors are written with arrows: $\vec{A}, \vec{B}$
• Components of vectors are written as small letters: $a_i, b_i$ where $i = 1,2,3$
• Basis is $(\vec{e_1}, \vec{e_2}, \vec{e_3})$

Notation		Meaning	Expansion (Cartesian coordinates)

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import React, { type PropsWithChildren } from "react";

type Props = {
  with: () => boolean;
} & PropsWithChildren

const Protected: React.FC<Props> = props =>
  props.with() ? <>{props.children}</> : <UserLogin />;

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cmake_minimum_required(VERSION 3.30)
project(project_cpp VERSION 0.1.0)

set(CMAKE_CXX_STANDARD 20)
set(CMAKE_CXX_STANDARD_REQUIRED ON)

SET(CMAKE_CXX_FLAGS "-Wall -Wextra -Werror" CACHE PATH "" FORCE)

set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/test/lib)
set(CMAKE_LIBRARY_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/test/lib)

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ThisBuild / version := "0.1.0-SNAPSHOT"

ThisBuild / scalaVersion := "3.4.0"

lazy val fpsCode = (project in file("."))
  .settings(
    name := "fps-code",
    idePackagePrefix := Some("ge.zgharbi.study.fps"),
    libraryDependencies ++= Seq(
      "org.scalameta" %% "munit" % "0.7.29" % Test,

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align.preset = none
# From https://scalameta.org/scalafmt/docs/configuration.html
#
# Keep in mind that 80 characters fit perfectly on a split laptop
# screen with regular resolution.
#
# GitHub mobile view only shows 80 characters and sometimes you might
# review code on your phone.
#
# Consider refactoring your code before choosing a value above 100.

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FROM alpine:3.10

ARG SPARK_VERSION=3.0.0-preview
ARG HADOOP_VERSION_SHORT=3.2
ARG HADOOP_VERSION=3.2.0
ARG AWS_SDK_VERSION=1.11.375

RUN apk add --no-cache bash openjdk8-jre python3

# Download and extract Spark

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import math
from dataclasses import dataclass
from math import sqrt

"""
    Scala-like case class pattern mathing in python >= 3.10
"""


@dataclass(frozen=True)

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import $ivy.`dev.zio::zio:1.0.0-RC8-12`
import $ivy.`dev.zio::zio-streams:1.0.0-RC8-12`

import zio._, zio.stream._

object Step1 {
  import java.nio.file.{Files, Paths, Path}
  import scala.collection.JavaConverters._
  import zio.blocking._

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import matplotlib.pyplot as plt
import pandas as pd
from pandas import DataFrame
from pandas.io.common import urlopen
import numpy as np

URL = "https://covidtracking.com/api/v1/states/daily.json"
ALPHA = 0.1
LOGARITHMIC = False