The imminent launch of XRISM will usher in an era of high-resolution X-ray spectroscopy. For active galactic nuclei (AGN) this is an exciting epoch that is full of massive potential for uncovering the ins and outs of supermassive black hole accretion. In this work, we review AGN research topics that are certain to advance in the coming years with XRISM and prognosticate the possibilities with Athena and Arcus. Specifically, our discussion focuses on: (i) the relatively slow moving ionised winds known as warm absorbers and obscurers; (ii) the iron emitting from different regions of the inner and outer disc, broad line region, and torus; and (iii) the ultrafast outflows that may be the key to understanding AGN feedback.

Tannaka Duality describes the relationship between algebraic objects in a given category and their representations; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful "fibre functors" to the category of vector spaces. We simultaneously generalize the theory of Tannaka duality in two ways: first, we replace Hopf algebras with weak Hopf algebras and strong monoidal functors with separable Frobenius monoidal functors; second, we replace the category of vector spaces with an arbitrary braided monoidal category. To accomplish this goal, we introduce a new graphical notation for functors between monoidal categories, using string diagrams with coloured regions. Not only does this notation extend our capacity to give simple proofs of complicated calculations, it makes plain some of the connections between Frobenius monoidal or separable Frobenius monoidal functors and the topology of the axioms defining certain algebraic structures. Finally, having generalized Tannaka to an arbitrary base category, we briefly discuss the functoriality of the construction as this base is varied.

SDSS J015957.64+003310.5 is an X-ray selected, $z=0.31$ AGN from the Stripe 82X survey that transitioned from a Type 1 quasar to a Type 1.9 AGN between 2000 and 2010. This is the most distant AGN, and first quasar, yet observed to have undergone such a dramatic change. We re-observed the source with the double spectrograph on the Palomar 5m telescope in July 2014 and found that the spectrum is unchanged since 2010. From fitting the optical spectra, we find that the AGN flux dropped by a factor of 6 between 2000 and 2010 while the broad H$\alpha$ emission faded and broadened. Serendipitous X-ray observations caught the source in both the bright and dim state, showing a similar 2-10 keV flux diminution as the optical while lacking signatures of obscuration. The optical and X-ray changes coincide with $g$-band magnitude variations over multiple epochs of Stripe 82 observations. We demonstrate that variable absorption, as might be expected from the simplest AGN unification paradigm, does not explain the observed photometric or spectral properties. We interpret the changing state of J0159+0033 to be caused by dimming of the AGN continuum, reducing the supply of ionizing photons available to excite gas in the immediate vicinity around the black hole. J0159+0033 provides insight into the intermittency of black hole growth in quasars, as well as an unprecedented opportunity to study quasar physics (in the bright state) and the host galaxy (in the dim state), which has been impossible to do in a single sources until now.