Higher category theory
higher category theory
Extra properties and structure
In higher category theory, the exchange law, or interchange law, states that the multiple ways of forming the composite of a pasting diagram of k-morphisms are equivalent.
The first exchange law (often called the exchange law) asserts that for composition of 2-morphisms we have an equivalence
asserting a compatibility of horizontal composition and vertical composition of 2-morphisms.
In a bicategory this equivalence is an identity. In even higher (and non-semi-strict) category theory, the interchange law becomes a higher morphism itself: the exchanger.
Combinatorics of exchange laws
One way to capture all exchange laws combinatorially is encoded by the cosimplicial -cateory that induces the homotopy coherent nerve. See there for more details on how this encodes the exchange laws.
Revised on August 31, 2010 04:53:16
by Urs Schreiber