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math.CT2025
Towards a Unified Theory of Time-Varying Data
Benjamin Merlin Bumpus, James Fairbanks, Martti Karvonen +2
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a gene…
math.CT2024
Inner automorphisms as 2-cells
Pieter Hofstra, Martti Karvonen
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connect…
math.CT2024
Inner autoequivalences in general and those of monoidal categories in particular
Pieter Hofstra, Martti Karvonen
We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how…