why my bibliography is not working?

Question

Here is the description of the book I am citing which I added in a different file named mybibliography.bib :

@book {MR2814476,
    AUTHOR = {Arkowitz, Martin},
     TITLE = {Introduction to homotopy theory},
    SERIES = {Universitext},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {xiv+344},
      ISBN = {978-1-4419-7328-3},
   MRCLASS = {55-02 (55Pxx)},
  MRNUMBER = {2814476},
MRREVIEWER = {Samuel B. Smith},
       DOI = {10.1007/978-1-4419-7329-0},
       URL = {https://doi-org.libproxy.library.wmich.edu/10.1007/978-1-4419-7329-0},
}

Here is my document from the beginning:

\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage[a4paper, margin=1in]{geometry}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
%\usepackage[ngerman]{babel}
\usepackage{tikz-cd}
\usepackage{makecell}
\usepackage{mathtools}
\usepackage{commath}
\usepackage{bbm}
\usetikzlibrary{babel}
 \usetikzlibrary{shapes.geometric}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{lipsum}
\usepackage{titlesec}
\usepackage{circledsteps}
\usepackage{ relsize, stackengine}
\usepackage[all,cmtip]{xy}
%\usepackage{natbib}
\usepackage[english]{babel}
\usepackage[backend=biber,style=alphabetic,sorting=ynt]{biblatex}
\usetikzlibrary{intersections}
%\newcommand{\circledell}{\stackinset{c}{}{c}{}{$ \ell $}{$\mathlarger{\bigcirc}$}}
\newtheorem{theorem}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem{definition}{Definition}[chapter]
\newtheorem{example}{Example}
\newtheorem{cor}{Corollary}
\newtheorem{question}{Question}
\usepackage[nottoc]{tocbibind} % For adding List of Tables and List of Figures to Table of Contents
\usepackage[titles]{tocloft}
\makeatletter
\def\ps@headings{%
      \def@oddfoot{\normalfont\hfil\thepage\hfil}%
      \def@evenfoot{\normalfont\hfil\thepage\hfil}}
      \def@evenhead{\hfil\slshape\leftmark}%
      \def@oddhead{{\slshape\rightmark}\hfil%
      \let@mkboth\markboth
    \def\chaptermark##1{%
      \markboth {\MakeUppercase{%
        \ifnum \c@secnumdepth >\m@ne
          \if@mainmatter
            @chapapp\ \thechapter. \ %
          \fi
        \fi
        ##1}}{}}%
    \def\sectionmark##1{%
      \markright {\MakeUppercase{%
        \ifnum \c@secnumdepth >\z@
          \thesection. \ %
        \fi
        ##1}}}}
\makeatother
\pagestyle{headings}% apply new definitions
\addbibresource{mybibliography.bib}

And here is the part of my code in which I am citing the book:

\textbf{Definition $3.1.3$}\\
If $(X', \varphi ')$ and $(X, \varphi )$ are co-H-spaces and $h: X' \rightarrow X$ is a map, we say that $h:(X', \varphi ') \rightarrow (X, \varphi )$ is a $\emph{co-H-map}$ if $\varphi h = (h \vee h) \varphi'$. You can also look at definition $, 2.2.8$ in $~\cite{MR2814476}$ to see this definition using a commutative diagram.

But I do not know why I did not get any references page showing my bibliography, can any tell me what is wrong in my code?

Also, what bibliography style am I allowed to do?

Answer 1

Since you're using biblatex and biber to create the bibliography, you need to furnish a \printbibliography statement to tell LaTeX where in the document the formatted bibliography should show up.

I would also recommend loading the xurl package, to allow line breaks in URL-like strings at arbitrary locations.

Somewhat curiously, while your preamble features the instruction

\newtheorem{definition}{Definition}[chapter]

you don't make use of it in the body the document.

A separate subject: You asked, "what bibliography style am I allowed to [use]?" Biblatex features lots and lots of style. Which ones you are either allowed to use or are required to use is something we know nothing about. I suggest you ask your publisher for advice on this issue.

\documentclass{book}
%% Aside: I've stripped the preamble down to the bare minimum
\begin{filecontents}[overwrite]{mybibliography.bib}
@book {MR2814476,
    AUTHOR = {Arkowitz, Martin},
     TITLE = {Introduction to Homotopy Theory},
    SERIES = {Universitext},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {xiv+344},
      ISBN = {978-1-4419-7328-3},
   MRCLASS = {55-02 (55Pxx)},
  MRNUMBER = {2814476},
MRREVIEWER = {Samuel B. Smith},
       DOI = {10.1007/978-1-4419-7329-0},
       URL = {https://doi-org.libproxy.library.wmich.edu/10.1007/978-1-4419-7329-0},
}
\end{filecontents}
\usepackage{amsthm}
\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]
\usepackage[a4paper, margin=1in]{geometry}
%\usepackage[utf8]{inputenc} % that's the default nowadays
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[english]{babel}
\usepackage{xurl} % allow arbitrary line breaks in URL-like strings
\usepackage[backend=biber,style=alphabetic,sorting=ynt]{biblatex}
\addbibresource{mybibliography.bib}
\begin{document}
\setcounter{chapter}{3}  % just for this example
\setcounter{section}{1}
\setcounter{definition}{2}
\begin{definition}
If $(X', \varphi ')$ and $(X, \varphi )$ are co-H-spaces and $h\colon X' \rightarrow X$ 
is a map, we say that $h\colon(X', \varphi ') \rightarrow (X, \varphi )$ is a $\emph{co-H-map}$ 
if $\varphi h = (h \vee h) \varphi'$. 
You can also look at definition 2.2.8 in~\cite{MR2814476} to see 
this definition using a commutative diagram.
\end{definition}
\printbibliography % tell LaTeX to print the formatted bibliography 
\end{document}