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Topos - Wikipedia In mathematics, a topos (US: ˈtɒpɒs , UK: ˈtoʊpoʊs, ˈtoʊpɒs ; plural topoi ˈtɒpɔɪ or ˈtoʊpɔɪ , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site) Topoi behave much like the category of sets and possess a notion of localization [1]
topos in nLab “Topos” is a Greek term intended to describe the objects studied by “analysis situs,” the Latin term previously established by Poincaré to signify the science of place [or situation]; in keeping with those ideas, a 𝒰 \mathcal{U}-topos was shown to have presentations in various “sites”
Topos Theory in a Nutshell - Department of Mathematics So what is a topos? A topos is category with certain extra properties that make it a lot like the category of sets There are many different topoi; you can do a lot of the same mathematics in all of them; but there are also many differences between them
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