标题： 等变拓扑和拓扑斯理论中的双重分解系统 显示英文标题

标题： Double factorization systems in equivariant topology and topos theory

摘要： 在本文中，我们研究双分解系统在Eilenberg-Moore（余）代数范畴中的扩展。 我们证明在范畴$\mathbf{Tych}$、$\mathbf{Unif}$和$\mathbf{Comp}$中的双分解系统$(\texttt{ExEpi},\texttt{Bim},\texttt{ExMono})$在相应的Eilenberg-Moore代数范畴$\mathbf{Tych}^{\mathbb{H}^t}$、$\mathbf{Unif}^{\mathbb{H}^u}$和$\mathbf{Comp}^{\mathbb{H}^c}$中扩展为相同的双分解系统。 我们建立了笛卡尔双分解系统与LT拓扑之间的联系。 我们提供了笛卡尔双分解系统在余代数到范畴中扩展的充分条件。 显示英文摘要

摘要： In the present work, we investigate the extension of double factorization systems to the categories of Eilenberg-Moore (co)algebras. We show that the double factorization systems $(\texttt{ExEpi},\texttt{Bim},\texttt{ExMono})$ in the categories $\mathbf{Tych}$, $\mathbf{Unif}$ and $\mathbf{Comp}$ extend to the same double factorization systems in the corresponding categories of Eilenberg-Moore algebras $\mathbf{Tych}^{\mathbb{H}^t}$, $\mathbf{Unif}^{\mathbb{H}^u}$ and $\mathbf{Comp}^{\mathbb{H}^c}$. We establish a connection between cartesian double factorization systems and LT-topologies. We provide sufficient conditions for the extension of cartesian double factorization systems to the topos of coalgebras.