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Online seminář z algebry - 15.10.2020 PDF Tisk

Další seminář z algebry se koná 15.10.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Taichi Uemura

The universal exponentiable arrow

Abstrakt:
Cartmell showed that the category of generalized algebraic theories is equivalent to the category of contextual categories. This implies that the theory of generalized algebraic theories is essentially algebraic. We characterize the essentially algebraic theory of generalized algebraic theories as the free category with finite limits and with an exponentiable arrow.

The main theorem and a syntactic proof are found in arXiv:2001.09940. In this talk we give a semantic proof.

Aktualizováno Středa, 14 Říjen 2020 15:24
 
Online seminář z algebry - 8.10.2020 PDF Tisk

Další seminář z algebry se koná 8.10.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Christina Vasilakopoulou

Oplax Hopf Algebras

Abstrakt:
Hopf categories were introduced by Batista, Caenepeel and Vercruysse in 2016, as a many-object generalization of Hopf algebras linked to other notions like multiplier Hopf algebras and with applications to categorical Galois theory. What is of particular interest is that the multiplication and comultiplication appear to make use of different monoidal products: Gabriella Bohm in subsequent work expressed Hopf categories as specific opmonoidal monads. In our work, we follow a different direction of generalizing Hopf monoids in a braided monoidal bicategory, that allows us to realize Hopf categories as Hopf-type objects over the same monoidal product, restoring in a sense the self-dual feature of classical Hopf algebras. In this talk, we introduce oplax bimonoids and oplax Hopf monoids in an arbitrary braided monoidal bicategory, we study their main properties and we exemplify such structures in a Span-type bicategory where they return semi-Hopf and Hopf categories.

This is a report on joint work with Mitchell Buckley, Timmy Fieremans and Joost Vercruysse.

Aktualizováno Středa, 07 Říjen 2020 15:14
 
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