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| Oct 3 |
Thu |
Adrian Miranda (Manchester) |
Topology Seminar |
| 16:00 |
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Tricategorical Universal Properties Via Enriched Homotopy Theory
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Hicks Seminar Room J11 |
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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 |
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Hicks Seminar Room J11 |
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| Oct 17 |
Thu |
Daniel Graves (Leeds) |
Topology Seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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| Oct 31 |
Thu |
Emily Roff (Edinburgh) |
Topology Seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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| Nov 7 |
Thu |
Cheuk Yu Mak (Sheffield) |
Topology Seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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| Nov 21 |
Thu |
Willow Bevington (Edinburgh) |
Topology Seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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| Nov 28 |
Thu |
Oscar Randal-Williams (Cambridge) |
Topology Seminar |
| 16:00 |
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Configuration spaces as commutative monoids
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Hicks Seminar Room J11 |
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Abstract:
The 1-point compactification of the space of unordered configurations of n points in a compact manifold M is well-known to be homotopy invariant in M. In fact the collection of all these spaces have further structure: they form a commutative monoid object, by superposition of configurations. I will show how this commutative monoid object has a simple (derived) presentation, and explain various consequences for the homology of configuration spaces which can be derived from this.
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| Dec 5 |
Thu |
Gong Show |
Topology Seminar |
| 15:00 |
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Hicks Seminar Room J11 |
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| Dec 12 |
Thu |
Constanze Roitzheim (Kent) |
Topology Seminar |
| 16:00 |
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Homotopy theory of finite total orders, trees and chicken feet
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Hicks Seminar Room J11 |
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Abstract:
A transfer system is a graph on a lattice satisfying certain restriction and composition properties. They were first studied on the lattice of subgroups of a finite group in order to examine equivariant homotopy commutativity, which then unlocked a wealth of links to combinatorial methods.
On a finite total order [n], transfer systems can be used to classify different homotopy theories on [n]. The talk will involve plenty of examples and not assume any background knowledge.
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| Dec 19 |
Thu |
Martin Palmer (Leeds/Bucharest) |
Topology Seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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