# Notes and Miscellaneous

**Cauchy-complete categories and lax additivity**

Notes (pdf, 1.533kB) and Proof Compendium (pdf, 472kB)

Supplementary Material to a Seminar Talk I gave in the "Higher Structures" Seminar 2024 in Hamburg. Using the technology of Cauchy-complete enriched ∞-categories, I give a very conceptual proof of the universal characterization of the (∞,2)-category of profunctors as the free lax semiadditive category, up to idempotent completion. I generalize it to enriched profunctors and skech a connection to (higher) multifusion categories.

**Cauchy-completions and higher idempotents**

Notes: Cauchy-completions and higher idempotents (pdf, 1.200kB)

Notes to an online talk I gave at the Mathematical Physics group seminar in Vienna 2024. I introduce the notions of Cauchy-complete categories and absolute colimits, go through several examples, and elaborate their application to phyics through higher idempotents and higher multifusion categories.

**Functor of Points and Superschemes**

Functor of Points and Superschemes (pdf, 502kB)

Notes to a Seminar Talk I gave in the Seminar "Supergeometry" 2021 in Heidelberg. Including an introduction to the Yoneda Lemma, and applications of the Functor-of-Points point of view on (Super-)manifolds and (Super-)schemes.