Title: Cartesian versus monoidal categories: the tensor product of algebraic structures in a general setting
Speaker: Joaquín Diaz-Boils (Pontifical Catholic University of Ecuador, Quito, Ecuador)
Abstract: Considering the tensor product of algebraic structures, rings in particular, as a motivating example, we define the concepts of Monoidal and Symmetric Monoidal Category. Then, a comparative study of their relation with the concrete setting of Cartesian Category is developed establishing the conditions for a Monoidal Category to become Cartesian. In this line it will be presented minimum conditions to obtain a Cartesian Monoidal Category. Finally we give some examples, in particular the category of cocommutative comonoids, as a way to define a Cartesian Category living into a Symmetric Monoidal one.
