# Functoriality of colored link homologies

## TL;DR

This paper proves that certain advanced link invariants, specifically the bigraded colored Khovanov-Rozansky invariants, are functorial under link and tangle cobordisms, establishing a key property in knot theory.

## Contribution

It demonstrates the functoriality of bigraded colored Khovanov-Rozansky link and tangle invariants, a significant advancement in understanding their structural properties.

## Key findings

- Proved functoriality of bigraded colored Khovanov-Rozansky invariants
- Established invariants' behavior under link and tangle cobordisms
- Enhanced the theoretical framework of link homologies

## Abstract

We prove that the bigraded colored Khovanov-Rozansky type A link and tangle invariants are functorial with respect to link and tangle cobordisms.

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Source: https://tomesphere.com/paper/1703.06691