\usepackage[utf8]{inputenc}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{mathrsfs}

\usepackage{tikz}

\usetikzlibrary{cd}

\newcommand*{\ca}[1]{\ensuremath{\mathbf{#1}}}
\newcommand*{\idarr}[1]{\ensuremath{\mathrm{id}_{#1}}}

\newcommand{\id}{\ensuremath{\mathrm{id}}}
\renewcommand{\implies}{\ensuremath{\rightarrow}}

\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\arr}[3]{\begin{tikzcd}[ampersand replacement=\&]{#1} \rar{#2} \& {#3}\end{tikzcd}}