| Version 10 |
Version 9 |
| \begin{definition} |
\begin{definition} |
| A \emph{$C_1$-category} is defined as a category $\mathcal{C}_1$ that |
A \emph{$C_1$-category} is defined as a category $\mathcal{C}_1$ that |
| for every family of monomorphisms $\left\{u_i: A_i \to B_i\right\}$ the morphism |
for every family of monomorphisms $\left\{u_i: A_i \to B_i\right\}$ the morphism |
|
$$\iota = \oplus u_i: \oplus A_i \to A_i \times \oplus B_i $$
|
$$\iota = \oplus u_i: \oplus A_i \to \times \oplus B_i $$
|
| is also a monomorphism (\cite{BM266}). |
is also a monomorphism (\cite{BM266}). |
| \end{definition} |
\end{definition} |
|
|
| \begin{remark} |
\begin{remark} |
| With certain additional conditions (as explained in ref. \cite{BM266}) $\mathcal{C}_1$ may satisfy the Grothendieck axiom $\mathcal{A}b5$, thus becoming a |
With certain additional conditions (as explained in ref. \cite{BM266}) $\mathcal{C}_1$ may satisfy the Grothendieck axiom $\mathcal{A}b5$, thus becoming a |
| $C_3$-category (Ch. 11 in \cite{BM266}). |
$C_3$-category (Ch. 11 in \cite{BM266}). |
| \end{remark} |
\end{remark} |
|
|
| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{BM266} |
\bibitem{BM266} |
| See p.81 in ref. $[266]$ in the |
See p.81 in ref. $[266]$ in the |
| \PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
\PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
|
|
| \bibitem{NP288} |
\bibitem{NP288} |
| Ref. $[288]$ in the \PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
Ref. $[288]$ in the \PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
|
|
| \end{thebibliography} |
\end{thebibliography} |
