17 citations · 98 across the 21 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
The Way of the Dagger
Martti Karvonen
A dagger category is a category equipped with a functorial way of reversing morphisms, i.e. a contravariant involutive identity-on-objects endofunctor. Dagger categories with addit…
Limits in dagger categories
Chris Heunen, Martti Karvonen
We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up…
Biproducts without pointedness
Martti Karvonen
We show how to define biproducts up to isomorphism in an arbitrary category without assuming any enrichment. The resulting notion coincides with the usual definitions whenever all…
Monads on dagger categories
Chris Heunen, Martti Karvonen
The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when everything respects the dagger: the monad and…