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Online seminář z algebry - 17.12.2020 |
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Další seminář z algebry se koná 17.12.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde. Gabriele Lobbia (University of Leeds)
Distributive Laws for Relative Monads
Abstrakt:
Monads are useful tools both in mathematics (especially in universal algebra) and in computer science. An important notion is that of a distributive law between two monads, which goes back to fundamental work of Jon Beck in the late '60s. This notion describes how two monads can interact with each other, an analogue of the ring distributivity of product over sum.
In recent years, a generalisation of monads has been studied, relative monads, where we drop the endofunctor requirement. This definition relies on an extension operator instead of a multiplication. We will start by reviewing the notion of distributive law. Then we will introduce relative monads and see what the right counterpart of distributive laws is when we consider a monad and a relative monad.
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Aktualizováno Středa, 16 Prosinec 2020 11:10 |
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Online seminář z algebry - 10.12.2020 |
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Další seminář z algebry se koná 10.12.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde. John Bourke (Masaryk University)
Accessible Infinity-Cosmoi
Abstrakt:
Riehl and Verity introduced infinity-cosmoi - certain simplicially enriched categories - as a framework in which to give a model-independent approach to infinity categories. For instance, there is an infinity cosmos of infinity-categories with finite limits or colimits, or of cartesian fibrations. In this talk, I will introduce the notion of an accessible infinity-cosmos and explain that most, if not all, infinity-cosmoi arising in practise are accessible. Applying results of earlier work, it follows that accessible infinity-cosmoi have homotopy weighted colimits and admit a broadly applicable homotopical adjoint functor theorem. This is a report on joint work with Steve Lack, and builds on recent work with Lack and Lukáš Vokřínek.
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Aktualizováno Středa, 09 Prosinec 2020 10:21 |
