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- Mat́ıas Menni
- 2000

We prove that the monoidal 2-category of cospans of ordinals and sur-jections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.

We prove that the monoidal 2-category of cospans of finite linear orders and surjections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.

- Matı́as Menni, G. Rosolini
- 2006

Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra's… (More)

- Mat́ıas Menni, Celia Magno
- 1999

Many categories of interest arise as exact completions of a left exact category. For example, for every small left exact category C, the presheaf topos Sets C op is an exact completion [1]. Realizability toposes are also examples [4]. More recently, in computer science there has been a lot of interest in the exact completion of the category of topological… (More)

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