Oct 3 | Thu | Adrian Miranda (Manchester) | Topology Seminar | ||
16:00 | Tricategorical Universal Properties Via Enriched Homotopy Theory | ||||
Hicks Seminar Room J11 | |||||
Abstract: When considering (co)limits of categories, one might ask for (co)cones to only commute up to natural isomorphism, or for universal properties to only hold up to equivalences of categories. In a general bicategory K such universal properties are modelled by the notion of a bicategorical (co)limit, where equations/relations are only ever imposed on data in the highest available dimension. However, these notions can also be modelled up to equivalence via ordinary (co)limits enriched over V= Cat, provided that one restricts their attention to weights that are well behaved with respect to the canonical monoidal model structure on V. In this talk I will explain how the above story adapts to the setting involving (co)limits *of* two-dimensional categories (or more generally, *in* three-dimensional categories). This involves homotopically well-behaved (co)limits enriched over the base V now given by Lack's monoidal model structure on the category of 2-categories and 2-functors. Running examples for motivation include Kleisli and Eilenberg-Moore constructions for pseudomonads, including for those on monoidal bicategories, as well as strictification constructions on bicategories and pseudo-double categories. This talk is based on my recent preprint. |
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Oct 10 | Thu | James Cranch (Sheffield) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Oct 17 | Thu | Daniel Graves (Leeds) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Oct 31 | Thu | Emily Roff (Edinburgh) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Nov 7 | Thu | Willow Bevington (Edinburgh) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Nov 28 | Thu | Oscar Randal-Williams (Cambridge) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Dec 5 | Thu | Martin Palmer (Bucharest/Leeds) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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Dec 12 | Thu | Constanze Roitzheim (Kent) | Topology Seminar | ||
16:00 | |||||
Hicks Seminar Room J11 | |||||
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