|
Online algebra seminar - March 11th, 1pm |
 |
 |
|
We will continue online on Thursday, March 11th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Eric Faber
Simplicial Moore paths are polynomial
Abstract:
In this talk I will show that the simplicial Moore path functor, first defined by Van den Berg and Garner, is a polynomial functor. This result, which surprised us a bit at first, has helped a great deal in developing effective Kan fibrations for simplicial sets. Based on joint work with Van den Berg. |
|
Last Updated on Wednesday, 10 March 2021 08:22 |
|
Online algebra seminar - March 4th, 1pm |
|
|
|
We will continue online on Thursday, March 4th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Chaitanya Subramaniam
Dependently typed algebraic theories
Abstract:
For S a set, S-sorted algebraic (or "Lawvere") theories are, equivalently, finite-product categories whose objects are freely generated by S, finitary monads on Set/S, or monoids in a category of "S-coloured cartesian collections".
When S is a suitable direct category, I will describe equivalences of categories between finitary monads on [S^op, Set], monoids in a category of "S-coloured cartesian collections", and a certain category of contextual categories (in the sense of Cartmell) under S^op.
Examples of such S are the categories of semi-simplices, globes and opetopes. Opetopes will be a running example, and we will see that there are three idempotent finitary monads on the category of opetopic sets, whose algebras are, respectively, small categories, coloured planar Set-operads, and planar coloured combinads (in the sense of Loday).
This is partly joint work with Peter LeFanu Lumsdaine, and partly joint work with Cédric Ho Thanh.
|
|
Last Updated on Tuesday, 02 March 2021 10:57 |
|
Online algebra seminar - February 25th, 1pm |
|
|
|
We will continue online on Thursday, February 25th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Mike Lieberman
Induced stable independence, with applications
Abstract:
A stable independence relation on a category (a generalization of the model-theoretic notion of nonforking independence!) consists of a very special family of commutative squares, whose members have almost all the desirable properties of pushouts---this is exceedingly useful in categories in which pushouts do not exist. We describe conditions under which a stable independence notion can be transferred from a subcategory to a category as a whole, and derive the existence of stable independence notions on a host of categories of groups and modules. We thereby extend results of Mazari-Armida, who has shown that the categories under consideration are stable in the sense of Galois types. Time permitting, we will also show that, provided the underlying category is locally finitely presentable, the existence of a stable independence relation immediately yields stable independence relations in every finite dimension. This is joint work with J. Rosický and S. Vasey. |
|
Last Updated on Tuesday, 23 February 2021 15:16 |
|
Online algebra seminar - February 18th, 1pm |
|
|
|
We will continue online on Thursday, February 18th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Charles Walker
Distributive laws, pseudodistributive laws and decagons
Abstract:
The notion of a distributive law of monads was introduced by Beck [1], and gives a concise description of the data required to compose monads. In the two dimensional case, Marmolejo [4] defined pseudodistributive laws of pseudomonads (where the required diagrams only commute up to an invertible modification). However, this description requires a number of coherence conditions due to the extra data involved.
In this talk we give alternative definitions of distributive laws and pseudodistributive laws involving the decagonal coherence conditions which naturally arise when the involved monads and pseudomonads are presented in their extensive form [7, 3, 2, 6]. As an application, we show that of Marmolejo and Wood’s eight coherence axioms for pseudodistributive laws [5], three are redundant. We will then go on to give (likely) minimal definitions of distributive laws and pseudodistributive laws, which further simplify the coherence conditions involved in this extensive viewpoint.
References
[1] Jon Beck. Distributive laws. In Sem. on Triples and Categorical Homology Theory (ETH,
Zürich, 1966/67), pages 119–140. Springer, Berlin, 1969.
[2] M. Fiore, N. Gambino, M. Hyland, and G. Winskel. Relative pseudomonads, Kleisli bicate-
gories, and substitution monoidal structures. Selecta Math. (N.S.), 24(3):2791–2830, 2018.
[3] Ernest G. Manes. Algebraic theories. Springer-Verlag, New York-Heidelberg, 1976. Graduate
Texts in Mathematics, No. 26.
[4] F. Marmolejo. Distributive laws for pseudomonads. Theory Appl. Categ., 5:No. 5, 91–147,
1999.
[5] F. Marmolejo and R. J. Wood. Coherence for pseudodistributive laws revisited. Theory Appl.
Categ., 20:No. 5, 74–84, 2008.
[6] F. Marmolejo and R. J. Wood. No-iteration pseudomonads. Theory Appl. Categ., 28:No. 14,
371–402, 2013.
[7] Robert Frank Carslaw Walters. A categorical approach to universal algebra. PhD thesis, Australian National University, 1970. |
|
Last Updated on Tuesday, 16 February 2021 11:23 |
|
|
