# nLab multiplicative conjunction

### Context

#### Monoidal categories

monoidal categories

# Contents

## Idea

In linear logic/linear type theory, one of the two linear versions of conjunction is called the multiplicative conjunction and usually denoted “$\otimes$”. The analogous connective in relevance logic is sometimes called the intensional conjunction or the fusion or cotenability, and sometimes denoted “$\circ$”.

The categorical semantics of the multiplicative conjunction is as the tensor product with respect to a (symmetric) monoidal category structure on the collection of types.

If one retains of all conjunctions in linear logic only the multiplicative conjunction, then one speaks of the fragment of linear logic called multiplicative linear logic or multiplicative intuitionistic linear logic or MILL for short. See also at linear type theory for more on this.

Last revised on May 3, 2016 at 19:22:31. See the history of this page for a list of all contributions to it.