**Yorkshire and Midlands Category Theory
Seminar**

Meeting 25

September 14th, 2021

Hosted on Zoom by the University of Leeds

Supported by the London Mathematical Society

**Schedule (all UK ****BST times)**

15:00-16:00 Caterina Consani (Johns Hopkins University) - On absolute geometry

16:00-16:05 Break

16:05-17:05 André Joyal (Université du Québec à Montréal) - A 2-categorical model of
1-cobordisms and the cyclic category Λ

17:05-17:10 Break

17:10-18:10 Peter May (University of Chicago) - A graded
monoid of multicategorical 2-monads

18:10-18:30 Discussion

All talks are 50 minutes followed by 10 minutes of questions.

**Abstracts**

**Speaker:** Caterina Consani (Johns Hopkins University)

**Title:** On absolute geometry.

**Abstract:** The talk
will overview some geometric constructions aiming to define the
notion of the absolute geometric point and the arithmetic
over it (joint with A. Connes).

**Slides:** here.

**Speaker:** André
Joyal (Université
du Québec
à Montréal)

**Title:** A 2-categorical model of 1-cobordisms and the
cyclic category Λ.

**Abstract:** See here.

**Speaker:** Peter May (University of
Chicago)

**Title:** A graded monoid of multicategorical 2-monads

**Abstract:** I will present some general category theory
that grew out of equivariant muliplicative infinite loop space
theory. We start from operads in a suitable 2-category of
internal categories. Such operads give rise to categories of
operators. With suitable multiplicative structure, algebras over
these give "symmetric monoidal graded 2-categories", which have
associated multicategories. These structures arise "in
nature", at least if nature includes stable homotopy
theory. From this starting point, we construct graded
multicategories of 2-monads (the monoids of the title) and show
how to use Lack's codescent objects to simultaneously strictify
and simplify this structure, making it relatively
concrete. The construction eliminates all pseudofunctors
from the picture and reduces from general categories of
operators to the simplest possible one, namely that given by the
category of finite based sets.

**Slides:** here.

Organizers

Nicola Gambino (University of Leeds)

Simona Paoli (University of Aberdeen)

Steve Vickers (University of Birmingham)

Page
last modified on September 15th, 2021 by Nicola Gambino