Topic
Diagonal functor
About: Diagonal functor is a research topic. Over the lifetime, 7 publications have been published within this topic receiving 22 citations.
Papers
1 Jan 2013
TL;DR: In this paper, a model structure for bisimplicial presheaves with weak equivalences dened by the diagonal functor and the cobrations are monomorphisms is introduced.
Abstract: The category of bisimplicial presheaves carries a model structure for which the weak equivalences are dened by the diagonal functor and the cobrations are monomorphisms. This model structure has the most cobrations of a large family of model structures with weak equivalences dened by the diagonal. The diagonal struc- ture for bisimplicial presheaves specializes to a diagonal model structure for bisimplicial sets, for which the brations are the Kan brations.
6 citations
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TL;DR: Any two deductions with the same premises and the same conclusions become equal because of a simple fact concerning adjunction with a full and faithful functor applied to the adjunction between the diagonal functor and the product biendofunctor, which corresponds to the conjunction connective.
Abstract: Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with the same premises and the same conclusions become equal. In terms of categorial proof theory, this is a consequence of a simple fact concerning adjunction with a full and faithful functor applied to the adjunction between the diagonal functor and the product biendofunctor, which corresponds to the conjunction connective.
5 citations
TL;DR: In this paper, it was shown that the diagonal functor that takes a multicosimplicial object in a model category to its diagonal cosimplicial objects is a right Quillen functor, which has applications to the calculus of functors.
Abstract: We show that the functor that takes a multicosimplicial object in a model category to its diagonal cosimplicial object is a right Quillen functor. This implies that the diagonal of a Reedy fibrant multicosimplicial object is a Reedy fibrant cosimplicial object, which has applications to the calculus of functors. We also show that, although the diagonal functor is a Quillen functor, it is not a Quillen equivalence for multicosimplicial spaces. We also discuss total objects and homotopy limits of multicosimplicial objects. We show that the total object of a multicosimplicial object is isomorphic to the total object of the diagonal, and that the diagonal embedding of the cosimplicial indexing category into the multicosimplicial indexing category is homotopy left cofinal, which implies that the homotopy limits are weakly equivalent if the multicosimplicial object is at least objectwise fibrant.
2 citations
Posted Content•
TL;DR: In this article, it was shown that the diagonal functor of a Reedy fibrant multicosimplicial object is a right Quillen functor, which has applications to the calculus of functors.
Abstract: We show that the functor that takes a multicosimplicial object in a model category to its diagonal cosimplicial object is a right Quillen functor. This implies that the diagonal of a Reedy fibrant multicosimplicial object is a Reedy fibrant cosimplicial object, which has applications to the calculus of functors. We also show that, although the diagonal functor is a Quillen functor, it is not a Quillen equivalence for multicosimplicial spaces.
We also discuss total objects and homotopy limits of multicosimplicial objects. We show that the total object of a multicosimplicial object is isomorphic to the total object of the diagonal, and that the diagonal embedding of the cosimplicial indexing category into the multicosimplicial indexing category is homotopy left cofinal, which implies that the homotopy limits are weakly equivalent if the multicosimplicial object is at least objectwise fibrant.
1 citations
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1 Jan 2014
TL;DR: In this paper, it was shown that any two deductions with the same premises and the same conclusions become equal, and this is a consequence of a simple fact concerning adjunction with a full and faithful functor applied to the adjunction between the diagonal functor and the product biendofunctor, which corresponds to the conjunction connective.
Abstract: Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with the same premises and the same conclusions become equal. In terms of categorial proof theory, this is a consequence of a simple fact concerning adjunction with a full and faithful functor applied to the adjunction between the diagonal functor and the product biendofunctor, which corresponds to the conjunction connective.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2015 | 1 |
| 2014 | 2 |
| 2013 | 1 |
| 2009 | 1 |
| 2007 | 1 |