Abstract: <\/strong>Principal bundles over topological spaces are among the most studied objects in geometry and topology. In this talk we will present a new notion of principal bundle that makes sense in any site that has all pullbacks and a terminal object, and we will use it to generalize quotient stacks. The topological group involved in the standard notion of principal bundle becomes in general a group object in the category and the notion of locally trivial morphism is generalized considering pullbacks along the morphisms of a covering family for the Grothendieck topology.<\/p>\nAfter recalling some basic notions that will be useful throughout the talk, we will present generalized principal bundles and we will see that they reduce to the classical principal bundles when the site is
\n(Top, std), where Top is the category of compactly generated topological spaces and std is the standard Grothendieck topology, i.e. the covering families of a topological space coincide with its open coverings.<\/p>\n
We will then use generalized principal bundles to construct generalized quotient prestacks and we will see a sketch of the proof of the fact that these new objects are indeed prestacks. Among generalized quotient prestacks, we will also consider the important particular case of classifying prestacks. We will conclude the talk presenting the main theorem, that states that, if the site is subcanonical and the underlying category satisfies some mild conditions, generalized quotient prestacks are stacks. We will see the key ideas behind the proof of this result, that will involve some important properties of the canonical Grothendieck topology on a category.<\/p>\n
<\/p>\n
Speaker: Ben Horton<\/strong>
\nTitle: Manifolds, Cobordisms, Braids and Loop Braids<\/strong><\/p>\nAbstract:<\/strong> We consider a categorified version of the category of manifolds and cobordisms, in the form of a pseudo-double category of manifolds, collared cobordisms, and equivalence classes of certain collar compatible diffeomorphisms between cobordisms. We discuss why this is the appropriate setting to formulate the monoidal categories of generalised braids and loop braids. We aim to give a pedagogical talk, and we will not assume previous knowledge on topological quantum field theory.<\/p>\nSpeaker: Ioannis Markakis<\/strong>
\nTitle: Computads for Generalised Signatures<\/strong><\/p>\nAbstract:<\/strong> In this talk, I will introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Structures for such a signature are presheaves with an interpretation of every function symbol of the signature, and I will describe how computads give rise to signatures. Generalising work of Batanin, I will sketch how computads with certain structure preserving morphisms form a presheaf category, and describe a forgetful functor from structures to computads. Structures free on a computad turn out to be the cofibrant objects for certain cofibrantly generated factorisation system, and the adjunction above induces the universal cofibrant replacement, in the sense of Garner, for this factorisation system. Finally, time-permitting, I will explaine how weak \u03c9-categoriesand algebraic semi-simplicial Kan complexes are structures of such signatures.<\/p>\nSpeaker: Ayberk Tosun<\/strong>
\nTitle: Patch Locale of a Spectral Locale in Univalent Type Theory<\/strong><\/p>\nAbstract:<\/strong> Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. The coreflector is what is called the patch locale: the pointfree analogue of the patch topology. A proof of this coreflection was given by Escard\u00f3 in the impredicative setting of the internal language of an elementary topos. Escard\u00f3's proof can be easily translated to univalent type theory using resizing axioms. In this talk, I will present our work with Mart\u00edn Escard\u00f3 on achieving this translation without using resizing axioms, by working with large, locally small, and small-complete frames with small bases. This question turns out to be nontrivial and involves predicative reformulations of several fundamental concepts of locale theory.<\/p>\n","protected":false},"excerpt":{"rendered":"Wednesday, 15 March 2023 Hosted by the University of Birmingham Supported by the London Mathematical Society Schedule: 13:00-13:45 Elena Caviglia 13:45-14:30 Benjamin Horton 14:30-15:00 Coffee Break 15:00-15:45 Ioannis Markakis 15:45-16:30 Ayberk Tosun Location: The meeting will be held in the Murray Learning Center (LC-UG10) at the University of Birmingham (A link to the campus map...","protected":false},"author":130,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-206","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/pages\/206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/comments?post=206"}],"version-history":[{"count":0,"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/pages\/206\/revisions"}],"wp:attachment":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/media?parent=206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}