Results

**1 - 1**of**1**### On Varieties of Closed Categories and Dependency of Diagrams of Canonical Maps ∗.

"... We present a series of diagrams Dn in Symmetric Monoidal Closed Categories such that there is infinitely many different varieties of SMCC (in the sense of universal algebra) defined by diagrams of this series as equations. Similar result will hold for weaker closed categories. We discuss the notion ..."

Abstract
- Add to MetaCart

(Show Context)
We present a series of diagrams Dn in Symmetric Monoidal Closed Categories such that there is infinitely many different varieties of SMCC (in the sense of universal algebra) defined by diagrams of this series as equations. Similar result will hold for weaker closed categories. We discuss the notion of dependency of diagrams in connection with this result. 1 Introduction. Canonical maps in closed categories may be seen as instances of morphisms of the free closed category generated by an infinite set of atoms. There exist many types of closed categories, for example Cartesian Closed Categories (CCC), Symmetric Monoidal Closed Categories (SMCC) etc. Closed