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pro vyhledávání: '"Osmond, Axel"'
Autor:
Osmond, Axel
We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of codescent o
Externí odkaz:
http://arxiv.org/abs/2204.06055
Autor:
Di Liberti, Ivan, Osmond, Axel
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in particular we
Externí odkaz:
http://arxiv.org/abs/2203.07046
Autor:
Osmond, Axel
We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prove it to be equivalent to a notion of bistable pseudofunctor, categorif
Externí odkaz:
http://arxiv.org/abs/2108.12697
Autor:
Osmond, Axel
We give an explicit description of the generator of finitely presented objects of the coslice of a locally finitely presentable category under a given object, as consisting of all pushouts of finitely presented maps under this object. Then we prove t
Externí odkaz:
http://arxiv.org/abs/2104.06537
Autor:
Caramello, Olivia, Osmond, Axel
With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, which we call the antecedent topology. Then we show that the associated s
Externí odkaz:
http://arxiv.org/abs/2104.05650
Autor:
Osmond, Axel
We give the site-theoretic account of the spectral construction as first introduced by Coste. We provide a detailed examination of the geometric properties of the spectrum, in particular what classes of topoi it produces when applied to the different
Externí odkaz:
http://arxiv.org/abs/2102.01259
Autor:
Osmond, Axel
This second part comes to the construction of the spectrum associated to a situation of multi-adjunction. Exploiting a geometric understanding of its multi-versal property, the spectrum of an object is obtained as the spaces of local units equipped w
Externí odkaz:
http://arxiv.org/abs/2012.02167
Autor:
Osmond, Axel
Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the case of a ri
Externí odkaz:
http://arxiv.org/abs/2012.00853
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