Talk:PlanetPhysics/Table of Categories

Original TeX Content from PlanetPhysics Archive
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\subsection{TABLE OF CATEGORIES} \begin{enumerate} \item (A / K), 3K (\htmladdnormallink{objects}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} over K) \item Ab,(\htmladdnormallink{Abelian groups}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}) \item AbTop,(abelian \htmladdnormallink{topological groups}{http://planetphysics.us/encyclopedia/PolishGroup.html}) \item AbTor,(abelian torsion \htmladdnormallink{groups}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}) \item Alg(1),(algebras with one unary \htmladdnormallink{operator}{http://planetphysics.us/encyclopedia/QuantumSpinNetworkFunctor2.html}) \item Alg(S2),(binary algebras) \item Alg(T),(\htmladdnormallink{T-algebras}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html}) \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 $+ ? + âˆ’ âˆ’ âˆ’$ \item reg. monadic $+ + + âˆ’ + +$ \item reg. algebraic $+ + + âˆ’ + +$ \item algebraic $+ + + âˆ’ + âˆ’$ \item essentially algebraic $+ + + âˆ’ âˆ’ âˆ’$ \item solid $+ + + âˆ’ âˆ’ âˆ’$ \item full refl. embedding $+ + + âˆ’ âˆ’ âˆ’$ \item adjoint $+ âˆ’ + âˆ’ âˆ’ âˆ’$ \item faithful $âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’$ \end{enumerate}

\subsection{FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES} \begin{enumerate} \item \textbf{monos extr. monos reg. monos epis extr. epis reg. epis isos} \item topological $+ âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’$ \item monadic $+ âˆ’ âˆ’ + + âˆ’ +$ \item reg. monadic $+ âˆ’ âˆ’ + + + +$ \item reg. algebraic $+ âˆ’ âˆ’ + + + +$ \item algebraic $+ âˆ’ âˆ’ + + + +$ \item ess. algebraic $+ âˆ’ âˆ’ + + âˆ’ +$ \item solid $+ âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’$ \item full refl. emb. $+ âˆ’ âˆ’ + + + +$ \item adjoint $âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ $ \item faithful $+ âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’$ \end{enumerate}

\subsection{TABLES OF FUNCTORS AND LIMITS}

\begin{enumerate} \item \textbf{creates, lifts, uniquely preserves, reflects} \item topological $ âˆ’ + + âˆ’$ \item monadic $+ + + +$ \item essentially algebraic $+ + + +$ \item solid, uniquely transp. $âˆ’ + + âˆ’$ \item adjoint $âˆ’ âˆ’ + âˆ’$ \end{enumerate}

\htmladdnormallink{Functors}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} AND COLIMITS \begin{enumerate} \item \textbf{lifts; uniquely preserves; detects:} \item topological $+ + +$ \item monadic $âˆ’ âˆ’ âˆ’$ \item solid $âˆ’ âˆ’ +$ \end{enumerate}

STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS

\begin{enumerate} \item \textbf{\htmladdnormallink{composition}{http://planetphysics.us/encyclopedia/Cod.html}; \htmladdnormallink{pushouts}{http://planetphysics.us/encyclopedia/Pushout.html}; co--intersections} \item \htmladdnormallink{isomorphisms}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} $+ + +$ \item \htmladdnormallink{retractions}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} $+ âˆ’ âˆ’$ \item reg. epis $âˆ’ + âˆ’$ \item strict epis $âˆ’ + +$ \item swell epis $+ + +$ \item strong epis $+ + +$ \item extr. epis $âˆ’ âˆ’ âˆ’$ \item epis $+ + +$ \end{enumerate}

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