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\section*{Algebraic Homotopy}

\hypertarget{algebraic_homotopy}{}\subsection*{{Algebraic homotopy}}\label{algebraic_homotopy}

This book by [[Baues]] gives an acoount of the author's interpretation of [[Henry Whitehead]]`s [[Algebraic Homotopy Theory]] as described in his ICM talk (1950) and his famous papers, \emph{[[Combinatorial homotopy I]]}, (1949), and \emph{[[Combinatorial homotopy II]]}, again (1949). Although the material contained in the first of these papers became central to the development of homotopy theory (CW complexes etc.) soon after its publication, the second paper, treating harder ideas including those of [[crossed complexes]], was relatively `unstudied' until much more recently. This book gives one interpretation of the ideas it developed from a modern point of view. That development continued in [[Combinatorial Homotopy and 4-Dimensional Complexes]].

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{algebraic_homotopy}{Algebraic homotopy}\dotfill \pageref*{algebraic_homotopy} \linebreak
\noindent\hyperlink{contents}{Contents}\dotfill \pageref*{contents} \linebreak
\noindent\hyperlink{preface}{Preface}\dotfill \pageref*{preface} \linebreak
\noindent\hyperlink{introduction}{Introduction}\dotfill \pageref*{introduction} \linebreak
\noindent\hyperlink{i_axioms_for_homotopy_theory_and_examples_of_cofibration_categories}{I Axioms for homotopy theory and examples of cofibration categories}\dotfill \pageref*{i_axioms_for_homotopy_theory_and_examples_of_cofibration_categories} \linebreak
\noindent\hyperlink{ii_homotopy_theory_in_a_cofibration_category}{II Homotopy theory in a cofibration category}\dotfill \pageref*{ii_homotopy_theory_in_a_cofibration_category} \linebreak
\noindent\hyperlink{iii_the_homotopy_spectral_sequences_in_a_cofibration_category}{III The homotopy spectral sequences in a cofibration category}\dotfill \pageref*{iii_the_homotopy_spectral_sequences_in_a_cofibration_category} \linebreak
\noindent\hyperlink{iv_extensions_coverings_and_cohomology_groups_of_a_category}{IV Extensions, coverings and cohomology groups of a category}\dotfill \pageref*{iv_extensions_coverings_and_cohomology_groups_of_a_category} \linebreak
\noindent\hyperlink{v_maps_between_mapping_cones}{V Maps between mapping cones}\dotfill \pageref*{v_maps_between_mapping_cones} \linebreak
\noindent\hyperlink{vi_homotopy_theory_of_cwcomplexes}{VI Homotopy theory of CW-complexes}\dotfill \pageref*{vi_homotopy_theory_of_cwcomplexes} \linebreak
\noindent\hyperlink{vii_homotopy_theory_of_complexes_in_a_cofibration_category}{VII Homotopy theory of complexes in a cofibration category}\dotfill \pageref*{vii_homotopy_theory_of_complexes_in_a_cofibration_category} \linebreak
\noindent\hyperlink{viii_homotopy_theory_of_postnikov_towers_and_the_sullivande_rham_equivalence_of_rational_homotopy_categories}{VIII Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories}\dotfill \pageref*{viii_homotopy_theory_of_postnikov_towers_and_the_sullivande_rham_equivalence_of_rational_homotopy_categories} \linebreak
\noindent\hyperlink{ix_homotopy_theory_of_reduced_complexes}{IX Homotopy theory of reduced complexes}\dotfill \pageref*{ix_homotopy_theory_of_reduced_complexes} \linebreak
\noindent\hyperlink{bibliography}{Bibliography}\dotfill \pageref*{bibliography} \linebreak
\noindent\hyperlink{index}{Index}\dotfill \pageref*{index} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


\hypertarget{preface}{}\subsection*{{Preface}}\label{preface}

\hypertarget{introduction}{}\subsubsection*{{Introduction}}\label{introduction}

\hypertarget{i_axioms_for_homotopy_theory_and_examples_of_cofibration_categories}{}\subsubsection*{{I Axioms for homotopy theory and examples of cofibration categories}}\label{i_axioms_for_homotopy_theory_and_examples_of_cofibration_categories}

\hypertarget{ii_homotopy_theory_in_a_cofibration_category}{}\subsubsection*{{II Homotopy theory in a cofibration category}}\label{ii_homotopy_theory_in_a_cofibration_category}

\hypertarget{iii_the_homotopy_spectral_sequences_in_a_cofibration_category}{}\subsubsection*{{III The homotopy spectral sequences in a cofibration category}}\label{iii_the_homotopy_spectral_sequences_in_a_cofibration_category}

\hypertarget{iv_extensions_coverings_and_cohomology_groups_of_a_category}{}\subsubsection*{{IV Extensions, coverings and cohomology groups of a category}}\label{iv_extensions_coverings_and_cohomology_groups_of_a_category}

\hypertarget{v_maps_between_mapping_cones}{}\subsubsection*{{V Maps between mapping cones}}\label{v_maps_between_mapping_cones}

\hypertarget{vi_homotopy_theory_of_cwcomplexes}{}\subsubsection*{{VI Homotopy theory of CW-complexes}}\label{vi_homotopy_theory_of_cwcomplexes}

\hypertarget{vii_homotopy_theory_of_complexes_in_a_cofibration_category}{}\subsubsection*{{VII Homotopy theory of complexes in a cofibration category}}\label{vii_homotopy_theory_of_complexes_in_a_cofibration_category}

\hypertarget{viii_homotopy_theory_of_postnikov_towers_and_the_sullivande_rham_equivalence_of_rational_homotopy_categories}{}\subsubsection*{{VIII Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories}}\label{viii_homotopy_theory_of_postnikov_towers_and_the_sullivande_rham_equivalence_of_rational_homotopy_categories}

\hypertarget{ix_homotopy_theory_of_reduced_complexes}{}\subsubsection*{{IX Homotopy theory of reduced complexes}}\label{ix_homotopy_theory_of_reduced_complexes}

\hypertarget{bibliography}{}\subsubsection*{{Bibliography}}\label{bibliography}

\hypertarget{index}{}\subsubsection*{{Index}}\label{index}

\hypertarget{references}{}\subsection*{{References}}\label{references}

\begin{itemize}%
\item \emph{Algebraic Homotopy}, Cambridge studies in advanced mathematics 15, Cambridge University Press, (1989).


\item [[Tim Porter]], \emph{Review of ``Algebraic Homotopy'` by H.J.Baues}, in Bull. London Math. Soc. 22 (1990) 196-197.



\end{itemize}


\end{document}