\contentsline {part}{I\hspace {1em}Fundamentals}{1}{}%
\contentsline {chapter}{\numberline {1}Categories}{3}{}%
\contentsline {section}{\numberline {1.1}Commutative diagrams}{5}{}%
\contentsline {section}{\numberline {1.2}Examples of categories}{5}{}%
\contentsline {subsection}{\numberline {1.2.1}Basic categories}{5}{}%
\contentsline {subsection}{\numberline {1.2.2}Classes of strucutres and spaces}{5}{}%
\contentsline {subsection}{\numberline {1.2.3}Alternative definition of structures and spaces}{6}{}%
\contentsline {section}{\numberline {1.3}Types of morphisms}{6}{}%
\contentsline {section}{\numberline {1.4}Types of categories}{8}{}%
\contentsline {subsection}{\numberline {1.4.1}Dual category}{8}{}%
\contentsline {section}{\numberline {1.5}Universal constructions}{9}{}%
\contentsline {subsection}{\numberline {1.5.1}Initial and terminal objects}{9}{}%
\contentsline {subsection}{\numberline {1.5.2}Product}{9}{}%
\contentsline {subsection}{\numberline {1.5.3}Equalizer}{10}{}%
\contentsline {subsection}{\numberline {1.5.4}Pullback}{11}{}%
\contentsline {chapter}{\numberline {2}Functors}{13}{}%
\contentsline {section}{\numberline {2.1}Diagram}{14}{}%
\contentsline {section}{\numberline {2.2}Cones}{14}{}%
\contentsline {section}{\numberline {2.3}Limit}{15}{}%
\contentsline {subsection}{\numberline {2.3.1}Pullback}{15}{}%
\contentsline {subsection}{\numberline {2.3.2}Limit}{15}{}%
\contentsline {chapter}{\numberline {3}Natural transformations}{17}{}%
\contentsline {section}{\numberline {3.1}Natural transformation}{17}{}%
\contentsline {section}{\numberline {3.2}Yoneda's lemma}{17}{}%