Coherence isomorphisms in the definition of the descent category.

Question

What does "modulo coherence isomorphisms" mean, in the definition of the descent category of a simplicial topos?

Answer 1

Equal modulo coherence isomorphisms means isomorphic in a specific way.

Higher category theory replaces the basic equations of category theory like $f\circ(g\circ h)=(f\circ g)\circ h$, with coherence isomorphisms like the isomorphism $f\otimes (g\otimes h)\to(f\otimes g)\otimes h$ of vector spaces. When two objects $X$ and $Y$ are equal modulo coherence isomorphisms, it means that there is a composition of coherence isomorphisms $X\to Y$.