Talk:PlanetPhysics/C2 Category

Original TeX Content from PlanetPhysics Archive

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\begin{document}

 In general, a \emph{$C_2$-category} is an $\mathcal{A}b4$-category, or, alternatively, an $\mathcal{A}b3$- and $\mathcal{A}b3^*$ -category $\C$ with certain additional conditions for the canonical \htmladdnormallink{morphism}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} from direct sums to products of any family of \htmladdnormallink{objects}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} in $\mathcal{C}$ \cite{NP288}).


\begin{definition}
A \emph{$C_2$-category} is defined as a \htmladdnormallink{category}{http://planetphysics.us/encyclopedia/Cod.html} $\mathcal{C}$ that has products, \htmladdnormallink{coproducts}{http://planetphysics.us/encyclopedia/Coproduct.html} and a zero object, and if the morphism $\iota : \oplus A_i \to \mathbf{X} A_i $ is a \htmladdnormallink{monomorphism}{http://planetphysics.us/encyclopedia/InjectiveMap.html} for any family of objects $\left\{A_i\right\}$ in $\mathcal{C}$ (p. 81 in \cite{BM266}).
\end{definition}

\begin{remark}
One readily obtains the result that a $C_2$-category is $C_1$ (\cite{BM266}).
\end{remark}

\begin{thebibliography}{9}
\bibitem{BM266}
Ref. $[266]$ in the
\htmladdnormallink{Bibliography for categories and algebraic topology}{http://planetphysics.us/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html}

\bibitem{NP288}
Ref. $[288]$ in the \htmladdnormallink{Bibliography for categories and algebraic topology}{http://planetphysics.us/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html}

\end{thebibliography} 

\end{document}