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Categorical rings were introduced by Jibladze and Pirashvili in their paper Third Mac Lane cohomology via categorical rings, Journal of Homotopy and related structures, 2, 2007, 187-216. We call those 2-rings. In these notes we present basic definitions and results regarding 2-modules. This is work in progress.
Indexed symmetric monoidal categories are an important refinement of bicategories -- this structure underlies several familiar bicategories, including the homotopy bicategory of parametrized spectra, and its equivariant and fiberwise generalizations.
We use Luries symmetric monoidal envelope functor to give two new descriptions of $infty$-operads: as certain symmetric monoidal $infty$-categories whose underlying symmetric monoidal $infty$-groupoids are free, and as certain symmetric monoidal $inf
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its domain, to be
We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids -- or in a straightforward generalisation, the category of modu
Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example a