arXiv subjects
Publications and source records attributed to Peter Bonart.
We introduce dependent adders. A dependent adder $A$ has for every $x \in A$ a way of adding together $x$ many elements of $A$. We provide examples from many disparate branches of mathematics. Examples include the field with one element $\mathbb{F}_1$, the real numbers with integrals as sums, the category of categories with oplax colimits as sums. We also consider modules over dependent adders and provide examples.
This paper proves a criterion for verifying the monoid axiom in enriched left Bousfield localizations.
Based on homological algebra of Grothendieck categories of enriched functors, two models for Voevodsky's category of big motives with reasonable correspondences are given in this paper.
Enriched motivic $\mathcal A$-spaces are introduced and studied in this paper, where $\mathcal A$ is an additive category of correspondences. They are linear counterparts of motivic $\Gamma$-spaces. It is shown that rational special enriched motivic $\widetilde{\mathrm{Cor}}$-spaces recover connective motivic bispectra with rational coefficients, where $\widetilde{\mathrm{Cor}}$ is the category of Milnor--Witt correspondences.
This paper shows that groups of order $64$ are uniquely determined up to isomorphism by their Tables of Marks. This then resolves a previously posed question about whether all groups of order less than $96$ are determined by their Tables of Marks.