论文标题
在本质上意味着本地连接的座椅上
Toposes over which essential implies locally connected
论文作者
论文摘要
我们介绍了eilc topos的概念：topos $ \ mathcal {e} $，以使每个基本几何形态与codomain $ \ mathcal {e} $都是本地连接的。然后，我们证明，如果$ x $是hausdorff（或更一般，如果$ x $是雅各布森），则拓扑空间上的带束带$ x $为eilc。 Grothendieck的进一步示例是EILC，是布尔式的Étendues，并分类了紧凑型组的座椅。接下来，我们介绍了CILC TOPOS的较弱概念：topos $ \ Mathcal {e} $，以使任何几何形态$ f：\ Mathcal {f} \ to \ Mathcal {e} $是本地连接的，一旦$ f^*$ f^*就是cartesian关闭。我们给出一些拓扑空间$ x $和小型类别的示例$ \ Mathcal {C} $，以便$ \ Mathbf {sh}（x）$ resp。 $ \ mathbf {psh}（\ mathcal {c}）$是cilc。最后，我们表明任何布尔基本拓扑都是CILC。
We introduce the notion of an EILC topos: a topos $\mathcal{E}$ such that every essential geometric morphism with codomain $\mathcal{E}$ is locally connected. We then show that the topos of sheaves on a topological space $X$ is EILC if $X$ is Hausdorff (or more generally, if $X$ is Jacobson). Further examples of Grothendieck toposes that are EILC are Boolean étendues and classifying toposes of compact groups. Next, we introduce the weaker notion of CILC topos: a topos $\mathcal{E}$ such that any geometric morphism $f : \mathcal{F} \to \mathcal{E}$ is locally connected, as soon as $f^*$ is cartesian closed. We give some examples of topological spaces $X$ and small categories $\mathcal{C}$ such that $\mathbf{Sh}(X)$ resp. $\mathbf{PSh}(\mathcal{C})$ are CILC. Finally, we show that any Boolean elementary topos is CILC.
