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Showing 2010 · math.CTShow all

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math.CT2010★ 13 cited

On the 2-categories of weak distributive laws

Gabriella Böhm, Stephen Lack, Ross Street

A weak mixed distributive law (also called weak entwining structure) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generali…

math.CT2010★ 15 cited

Enriched weakness

Stephen Lack, Jiri Rosicky

The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise whe…

math.CT2010★ 1 cited

On Cyclic Star-Autonomous Categories

Jeff Egger, Micah Blake McCurdy

We discuss cyclic star-autonomous categories; that is, unbraided star- autonomous categories in which the left and right duals of every object p are linked by coherent natural isom…

math.CT2010★ 6 cited

Levels in the toposes of simplicial sets and cubical sets

Carolyn Kennett, Emily Riehl, Michael Roy +1

The essential subtoposes of a fixed topos form a complete lattice, which gives rise to the notion of a level in a topos. In the familiar example of simplicial sets, levels coincide…

math.CT2010★ 89 cited

A Quillen model structure for Gray-categories

Stephen Lack

A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full sub…

math.CT2010★ 21 cited

Weak bimonads and weak Hopf monads

Gabriella Böhm, Stephen Lack, Ross Street

We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category M^T is monoidal and the forgetful functor from M^T to M is separa…