We introduce and study a multiparameter colored partition category CPar (x) by extending
the construction of the partition category, over an algebraically closed field k of characteristic …

In this thesis we are interested in studying derived categories of smooth projective varieties
over a field. Concretely, we study the geometric and categorical information from the variety …

One way to understand the deformation theory of a tensor category $ M $ is through its
Davydov-Yetter cohomology $ H_ {DY}^{\ast}(M) $ which in degree 3 and 4 is known to …

Theorem (Balmer [Bal02, Bal05]): Let Perf (X) be the derived category of perfect complexes
on a noetherian scheme equipped with the monoidal structure given by the derived tensor …

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full
theory of coalgebras: with counits and not necessarily locally conilpotent. For example …

For modules over Schur algebra, H. Krause defined a new “internal tensor product" using
the language of strict polynomial functors. We show that over an arbitrary commutative base …