We describe a new extension of the Todd–Coxeter algorithm adapted to computing left Kan extensions. The algorithm is a much simplified version of that introduced by Carmody and Walters (Category Theory, Proceedings of the International Conference Held in Como, Italy, 22–28 July 1990. Springer) in 1991. The simplification allows us to give a straightforward proof of its correctness and terminati...

We investigate the evolutionary history of the wide-ranging Nearctic treefrog Hyla arenicolor through the integration of extensive range-wide sampling, phylogenetic analyses of multilocus genetic data, and divergence dating. Previous phylogeographic studies of this frog documented a potential signature of introgressive hybridization from an ecologically and morphologically divergent sister spec...

We show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration. Mathematics Subject Classification 55R15 · 55R35 · 55U10 · 18C50

We investigated the role of commensals at the peak of infection with the colonic mouse pathogen Citrobacter rodentium. Bioluminescent and kanamycin (Kan)-resistant C. rodentium persisted avirulently in the cecal lumen of mice continuously treated with Kan. A single Kan treatment was sufficient to displace C. rodentium from the colonic mucosa, a phenomenon not observed following treatment with v...

Many program optimisations involve transforming a program in direct style to an equivalent program in continuation-passing style. This paper investigates the theoretical underpinnings of this transformation in the categorical setting of monads. We argue that so-called absolute Kan Extensions underlie this program optimisation. It is known that every Kan extension gives rise to a monad, the code...

An existing procedure to compute left Kan extensions over the ground category Set also computes left Kan extensions over the ground categories Cat, 2-Cat, n-Cat for any n and indeed !-Cat. Therefore extension data struc-tured in this manner already can make use of the left Kan extension notion of a best possible approximation. Examples include systems of labeled transition systems and certain h...

Institutions were introduced by Goguen and Burstall [GB84, GB85, GB86, GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality bet...

We showed previously that transcription of a plasmid-borne kan allele increases C-to-T mutations in the nontranscribed strand. Using two new plasmid-borne kan alleles, one cmp allele, and a chromosomal kan allele, we found in this study that transcription-induced mutations are not limited to specific genes, alleles, or locations and are likely to be a general property of transcript elongation i...