The theory of six functor formalisms is of high importance in geometric representation theory. Classically, one focuses in six functors on known cohomology theories such as coherent sheaves, étale sheaves or D-modules. However, thanks to the foundational work of Heyer--Mann on abstract six functor formalisms, and all the further advancements that have occurred since then, it is now possible to apply some of these techniques in rather general and abstract situations. Having such level of abstraction and generality could seem pretentious, but it turns out to be extremely useful in classical, but also complicate, frameworks of representation theory such as the theory of locally analytic p-adic representations. In this talk I will discuss the formalism behind scenes, namely the presentable category of kernels, and mention some applications to Cartier duality and the theory of locally analytic representations.