  This preprint comprises the first four out of five chapters of the Master's
thesis I wrote 2022 under the supervision of Catharina Stroppel and Paul
Wedrich at the University of Bonn titled "Categorified Jones-Wenzl projectors
and Generalizations". Chapter 1 can serve as introductory literature for
researchers or graduate students familiar with Schur-Weyl duality between the
symmetric group and the general linear Lie algebra or their quantum counter
parts, and who are seeking to learn a type B/D analogue of the famous type A
story. Chapter 1 serves as an introduction to the type B combinatorics and
blob-diagrammatics. Chapters 2,3, and 4 contain proofs of three main theorem
each - the first one is an explicit/computational proof of the easiest case of
quantum coideal Schur-Weyl duality involving non-trivial quantizations of
weight spaces, the second one shows the generalization of Jones-Wenzl
projectors to the type B Temperley-Lieb algebra and the third one uses
generalized Reidemeister moves and a functional analytic argument to prove a
version of the fact that powers of the type D full-twist converge towards the
type D Jones-Wenzl projector.
