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We show that the comma category $(mathcal{F}downarrowmathbf{Grp})$ of groups under the free group functor $mathcal{F}: mathbf{Set} to mathbf{Grp}$ contains the category $mathbf{Gph}$ of simple graphs as a full coreflective subcategory. More broadly, we generalize the embedding of topological spaces into Steven Vickers category of topological systems to a simple technique for embedding certain categories into comma categories, then show as a straightforward application that simple graphs are coreflective in $(mathcal{F}downarrowmathbf{Grp})$.
We study track categories (i.e., groupoid-enriched categories) endowed with additive structure similar to that of a 1-truncated DG-category, except that composition is not assumed right linear. We show that if such a track category is right linear up
We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematica
When $mathbb C$ is a semi-abelian category, it is well known that the category $mathsf{Grpd}(mathbb C)$ of internal groupoids in $mathbb C$ is again semi-abelian. The problem of determining whether the same kind of phenomenon occurs when the property
We generalise the construction of the Lie algebroid of a Lie groupoid so that it can be carried out in any tangent category. First we reconstruct the bijection between left invariant vector fields and source constant tangent vectors based at an ident
This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which emph{ex falso quodlibet} holds, how to convert it into a logic not satisfying this principle? We