Objet : Informations pour les catégoriciens en France et ailleurs
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- From: "Janelidze, Z, Prof []" <>
- To: Isar Stubbe <>, "" <>
- Subject: RE: [cat.fr] SIC à Calais le vendredi 8 octobre 2021
- Date: Fri, 3 Sep 2021 10:31:28 +0000
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Dear Andrée and Isar,
I would very much like to participate in SIC by videoconferencing. I would also very much like to give a talk, if possible. I have necessary equipment and a reliable fast internet connection to give a talk by videoconferencing.
Title: Forms vs monoidal categories
Abstract: By a “form” we mean a faithful amnestic functor. Such functors are of course a very old object of study. They arise naturally in categorical logic, categorical topology, as well as in the notion of a concrete category. In all of these topics, however, the emphasis is on the domain category of the functor. In the theory of forms, one regards the codomain of the functor as the main object of study, treating a form as an additional information that category is equipped with. This approach is very similar to the study of fibrations in topology and the original approach of Grothendieck in the theory of (categorical) fibrations. The fibres of a form are to be seen as abstractly specified posets of subobjects, quotient objects, or their combination. Functorial duality plays a significant role in the development of the theory: one is interested in axioms on a form that are invariant under switching to the dual form (functor). Forms have applications in the analysis of homomorphisms theorems for group-like structures in algebra, in the theory of semi-abelian categories, as well as in the theory of categorical closure operators. While we will mention some of these applications, the main purpose of this talk is to explain an analogy between forms seen as categories equipped with a “posetal structure” and monoidal categories. We will see, in particular, that these two structures provide two intermediate streams of structural hierarchy that exist between the notion of an abelian category and the notion of a general category.
With best regards, Zurab
From: <>
On Behalf Of Isar Stubbe
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- [cat.fr] SIC à Calais le vendredi 8 octobre 2021, Isar Stubbe, 03/09/2021
- RE: [cat.fr] SIC à Calais le vendredi 8 octobre 2021, Janelidze, Z, Prof [], 03/09/2021
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