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Idempotents in Tangle Categories Split

Ryan Blair

http://orcid.org/0000-0002-2547-8874

California State University, Long Beach, USA

E-mail Address: [email protected]

Corresponding author.

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and

Joshua Sack

California State University, Long Beach, USA

E-mail Address: [email protected]

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https://doi.org/10.1142/S0218216519500251Cited by:1 (Source: Crossref)

Abstract

In this paper, we use 3-manifold techniques to illuminate the structure of the category of tangles. In particular, we show that every idempotent morphism $A$ in such a category naturally splits as $A = B \circ C$ such that $C \circ B$ is an identity morphism.

Keywords:

AMSC: 57M99, 18D10

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