In category theory, objects are devoid of internal structure. We’ve seen however that in certain categories we can define relationships between objects that mimic the set-theoretic idea of one set being the su
In category theory, definitions, such as the definition of product and coproduct, depend not just on the objects but on the morphisms between them. In graph theory language, definitions depend not just on the nodes but also on the edges. Keep the same objects but define different morphisms ...
In category theory, objects are devoid of internal structure. We’ve seen however that in certain categories we can define relationships between objects that mimic the set-theoretic idea of one set being the subset of another. We do this using the subobject classifier. We would like to define...
Weber. "Multitensor lifting and strictly unital higher category theory". Theory Appl. Categ. 28.25 (2013), pp. 804-856.M. Batanin, D-C. Cisinski, and M. Weber. Multitensor lifting and strictly unital higher category theory. Theory and applications of categories, 28:804-856, 2013....
In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first principal result - the lifting theorem for multitensors - enables us to see the Gray tensor product of 2-...