To write triangle diagram with inclusion

Question

I want to write the following diagram. But I'm stuck with writing the map $\phi$ and inclusion one.

How can I draw the following diagram ? Thank you in advance.

My preamble is the following.

\documentclass[11pt,english]{smfart}
\usepackage[OT2,T1]{fontenc}
\usepackage[english]{babel}
\usepackage{url,xspace,smfthm}
%\usepackage{amsthm}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{mathtools}

\usepackage{tikz}
\usepackage{tikz-cd}
\usepackage{enumitem}


\DeclareSymbolFont{cyrletters}{OT2}{wncyr}{m}{n}
\DeclareMathSymbol{\Sha}{\mathalpha}{cyrletters}{"58}
\DeclareMathSymbol{\Zhe}{\mathalpha}{cyrletters}{"11}
\DeclareMathOperator{\Coker}{Coker}

\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{lem}{Lemma}
\newtheorem{cor}{Cor}
\newtheorem{remark}{remark}

\usetikzlibrary{cd,bbox,babel}

\usepackage{amsmath,amssymb,amsfonts,amscd}

Answer 1

Here's the CD:

\documentclass[11pt,english]{smfart}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}
O\ar[r]&A\ar[r]&B\ar[r]\ar[dr, "\phi", swap ]&C\ar[d, hook']\\
&&&P
\end{tikzcd}
\]
\end{document}

Off-topic: you should simplify your preamble loading only the necessary packages. For example, \usepackage{tikz-cd} is the same as

\usepackage{tikz}
\usetikzlibrary{cd}

you should use only one of the two alternatives.