Speaker: Markus Szymik
\nTitle: Categorical aspects of racks and quandles<\/strong><\/p>\nRacks and quandles are algebraic structures related to groups and symmetries. These concepts were rediscovered many times and have found applications across algebra, number theory, geometry, and topology. This talk shall be a friendly introduction to the categories of racks and quandles. The categorical bias brings problems. I will present solutions to some and mention others that are interesting.<\/p>\n
<\/p>\n
Speaker: Chiara Sarti<\/strong>
\nTitle: Posetal Diagrams for Logically-Structured Semistrict Higher Categories
\n<\/strong><\/p>\nThis talk will present some recent work with my supervisor Jamie Vicary.<\/p>\n
We now have a wide range of proof assis\u00adtants avail\u00adable for com\u00adpo\u00adsi\u00adtional rea\u00adson\u00ading in monoidal or higher categories which are free on some generat\u00ading sig\u00adna\u00adture. Motivated from categorical physics, we generalize the foun\u00adda\u00adtional math\u00ade\u00admat\u00adi\u00adcal for\u00admal\u00adism of the proof assistant homotopy.io, replacing the con\u00adven\u00adtional notion of string dia\u00adgram as a geo\u00admet\u00adri\u00adcal entity liv\u00ading inside an n-cube with a pose\u00adtal vari\u00adant that allows exotic branch\u00ading struc\u00adture. We show that these gen\u00ader\u00adal\u00adized diagrams have richer behav\u00adiour with respect to cat\u00ade\u00adgor\u00adi\u00adcal lim\u00adits, and give an algo\u00adrithm for com\u00adput\u00ading lim\u00adits in this set\u00adting, with a view towards future appli\u00adca\u00adtions.<\/p>\n
<\/p>\n
Speaker:\u00a0 Adrian Miranda<\/strong>
\nTitle: Weak-interchange based semi-strictification in low dimensional higher category theory
\n<\/strong><\/p>\nGiven a bicategory, its strictification can be described via a presentation in which the only relations are on 2-cells, or cells of the highest dimension. The freeness of the underlying category of of the strictification allows pseudofunctors to also be strictified to 2-functors; maps between 2-categories which preserve all operations of their domain on the nose. On the other hand, pseudonatural transformations cannot be made to respect the globular structure of their domain 2-categories on the nose. Via enrichment, this weakness precisely corresponds to the weakness present in a semi-strict model of three-dimensional categories known as a Gray-category.<\/p>\n
We will describe similar semi-strictification constructions for tricategories, presenting the example of fundamental trigroupoids of topological spaces. Once again, the underlying data of codimension one in the semi-strictification of any tricategory is free on the appropriate kind of generating data, i.e. a 2-computad. We use this to extend semi-strictification to higher dimensional maps between tricategories, or (3, k)-transfors, finding that trihomomorphisms strictify completely but that trinatural transformations only partially strictify. The resulting semi-strict trinatural transformations fail to be closed under composition, but upon closing them under composition we are able to form a closed structure on Gray-Cat, analogous to Gray's closed structure on 2-Cat. This is used to describe the hom-triequivalences of what is, conjecturally, a semi-strictification tetra-adjunction. We then consider certain well-behaved categories enriched over the closed structure on Gray-Cat, and use them to describe a construction which maps any weak four-dimensional category, or tetracategory, T to a semi-strictified structure T'. By construction there will be a tetrahomomorphism from T to T', and we conjecture that it is a tetraequivalence.<\/p>\n
<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"Monday, 19 June 2023 Hosted by the University of Leeds Supported by the London Mathematical Society Schedule: 13:00-14:00 Markus Szymik (Sheffield). 14:00 -- 14:30: Coffee break. 14:30\u201415:30\u00a0Chiara Sarti (Cambridge) 15:30 -- 16:00 Coffee break. 16:00 -- 17:00\u00a0Adrian Miranda (Manchester.) Location: The meeting will be held in the School of Mathematics at the University of Leeds...","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-211","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/pages\/211","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=211"}],"version-history":[{"count":0,"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/pages\/211\/revisions"}],"wp:attachment":[{"href":"https:\/\/conferences.leeds.ac.uk\/yamcats\/wp-json\/wp\/v2\/media?parent=211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}