Geodesic
Monic skeleta, Boundaries, Aufhebung, and the meaning of `one-dimensionality'
Theory and applications of categories, Tome 34 (2019), pp. 714-735.

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Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E \to S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form.
Publié le :
Classification : 18B25, 18F20
Keywords: Topos theory, Axiomatic Cohesion 
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     author = {Matias Menni},
     title = {Monic skeleta, {Boundaries,} {Aufhebung,} and the meaning of `one-dimensionality'},
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     volume = {34},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a24/}
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Matias Menni. Monic skeleta, Boundaries, Aufhebung, and the meaning of `one-dimensionality'. Theory and applications of categories, Tome 34 (2019), pp. 714-735. http://geodesic.mathdoc.fr/item/TAC_2019_34_a24/