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Stream: theory: category theory

Topic: Name for this operation? (Braided Monoidal)

Jacques Carette (Aug 03 2021 at 18:09):

Given a braided monoidal category with associator $\alpha$, braid $\sigma$, is there a common name (symbol?) for $\alpha \circ \sigma \otimes 1 \circ \alpha^{-1} : X \otimes (Y \otimes Z) \Rightarrow Y \otimes (X \otimes Z)$ ?

JS PL (he/him) (Aug 03 2021 at 19:39):

Actually, I believe the answer your looking for is in this paper: https://arxiv.org/pdf/1307.5969.pdf

Matteo Capucci (he/him) (Aug 04 2021 at 08:32):

I believe that has the type of a costrength for the self-action $\otimes$

Matteo Capucci (he/him) (Aug 04 2021 at 08:33):

Or at least that's what I call a natural morphism $X \bullet (Y \otimes Z) \to Y \otimes (X \bullet Z)$