We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we consider cartesian multicategories in a similar perspective and develop some peculiar items such as algebraic products. Several classical facts arise as a consequence of this analysis when some of the multicategories involved are representable.
Keywords: Sequential, representable, exponentiable and cartesian multicategories; preadditive, additive and finite product categories; Boardman-Vogt tensor product
2010 MSC: 18C10, 18D10, 18D50, 18D99, 18E05
Theory and Applications of Categories, Vol. 29, 2014, No. 19, pp 496-541.