Table of categories
TableOfCategories
2010-06-05 12:38:52
2010-06-05 12:41:54
Topic
categories
functors
categorical properties
\subsection{TABLE OF CATEGORIES}
\begin{enumerate}
\item (A / K), 3K (objects over K)
\item Ab,(abelian groups)
\item AbTop,(abelian topological groups)
\item AbTor,(abelian torsion groups)
\item Alg(1),(algebras with one unary operator)
\item Alg(S2),(binary algebras)
\item Alg(T),(T-algebras)
\item Alg(S),(S-algebras)
\item Alg(M),(M-algebras)
\item Aut,(automata)
\item Autr,(reachable automata)
\end{enumerate}
\subsection{TABLES OF FUNCTORS AND MORPHISMS: PRESERVATION PROPERTIES}
\begin{enumerate}
\item \textbf{monos extr.; monos reg.; monos epis; extr. epis; reg. epis}
\item topological $+ + + + + +$
\item monadic $+ ? + − − −$
\item reg. monadic $+ + + − + +$
\item reg. algebraic $+ + + − + +$
\item algebraic $+ + + − + −$
\item essentially algebraic $+ + + − − −$
\item solid $+ + + − − −$
\item full refl. embedding $+ + + − − −$
\item adjoint $+ − + − − −$
\item faithful $− − − − − −$
\end{enumerate}
\subsection{FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES}
\begin{enumerate}
\item monos extr. monos reg. monos epis extr. epis reg. epis isos
\item topological $+ − − + − − −$
\item monadic $+ − − + + − +$
\item reg. monadic $+ − − + + + +$
\item reg. algebraic $+ − − + + + +$
\item algebraic $+ − − + + + +$
\item ess. algebraic $+ − − + + − +$
\item solid $+ − − + − − −$
\item full refl. emb. $+ − − + + + +$
\item adjoint $− − − − − − $
\item faithful $+ − − + − − −$
\end{enumerate}
\subsection{TABLES OF FUNCTORS AND LIMITS}
\begin{enumerate}
\item \textbf{creates, lifts, uniquely preserves, reflects}
\item topological $ − + + −$
\item monadic $+ + + +$
\item essentially algebraic $+ + + +$
\item solid, uniquely transp. $− + + −$
\item adjoint $− − + −$
\end{enumerate}
FUNCTORS AND COLIMITS
\begin{enumerate}
\item \textbf{lifts; uniquely preserves; detects:}
\item topological $+ + +$
\item monadic $− − −$
\item solid $− − +$
\end{enumerate}
STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS
\textbf{composition; pushouts; cointersections}
\begin{enumerate}
\item isomorphisms $+ + +$
\item retractions $+ − −$
\item reg. epis $− + −$
\item strict epis $− + +$
\item swell epis $+ + +$
\item strong epis $+ + +$
\item extr. epis $− − −$
\item epis $+ + +$
\end{enumerate}