Date 
Topic and Recording Link 
21.04.2022 
Motivation from noncommutative geometry, Leavitt algebras, group rings, Morita equivalence 
25.04.2022 
Balanced tensor product, Hom, Eilenberg–Watts Theorem 
28.04.2022 
Morita equivalence through bimodules, examples, finitely generated project module, generator 
02.05.2022 
Morita equivalence, proof of criterion and 

Bicategories: motivation and data 
05.05.2022 
Bicategories: Coherence conditions, equivalences in bicategories 
09.05.2022 
Morphisms between bicategories, especially to Rings 
12.05.2022 
Morphisms to Rings as graded rings, some examples of morphisms 
16.05.2022 
Transformations between morphisms of bicategories: motivation, definition, case of Rings 
19.05.2022 
Transformations and graded modules, modifications between transformations, lax cones 
23.05.2022 
Lax covariant representations, lax covariance ring 
30.05.2022 
A case when all transformations are strong, actions of groups by Morita equivalences, fgp modules over C(X) 
02.06.2022 
Group action by Morita equivalences, twisted group action, projective representations 
09.06.2022 
Localisation at rings at elements, matrices, and maps of fgp modules 
10.06.2022 12–14 
Covariance rings as Cohn localisations, Leavitt path algebras as covariance rings 
17.06.2022 12–14 
Permutational bimodules over group rings, iterated monodromy group 
20.06.2022 
Selfsimilar group, iterated monodromy group, Grigorchuk group 
23.06.2022 
Composition of morphisms, isomorphism of bicategories 
24.06.2022 12–14  Representable homomorphisms, composition of transformations 
30.06.2022  Composition of modifications, equivalence of bicategories, bicategories of morphisms 
04.07.2022 
The Yoneda homomorphism, the Yoneda Lemma, part of its proof (no audio signal for about one hour) 
07.07.2022 
Proof of the Yoneda Lemma for bicategories (no audio signal for last 20 minutes) 
08.07.2022 12–14  Further details of the bicategorical Yoneda lemma, application to representations of homomorphisms, cones and lax cones 
14.07.2022 
Limits and colimits as parts of homomorphisms, whiskering transformations with morphisms 
18.07.2022 
Adjunctions between homomorphisms of bicategories, more compositions for transformations 
21.07.2022 
What has been achieved, what's still to be done? 