Geodesic
Coherence for Factorization Algebras
Theory and applications of categories, Tome 10 (2002), pp. 134-147

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

For the 2-monad $((-)^2,I,C)$ on CAT, with unit $I$ described by identities and multiplication $C$ described by composition, we show that a functor $F : {\cal K}^2 \rightarrow \cal K$ satisfying $FI_{\cal K} = 1_{\cal K}$ admits a unique, normal, pseudo-algebra structure for $(-)^2$ if and only if there is a mere natural isomorphism $F F^2 \rightarrow F C_{\cal K}$. We show that when this is the case the set of all natural transformations $F F^2 \rightarrow F C_{\cal K}$ forms a commutative monoid isomorphic to the centre of $\cal K$.

Classification : 18A32, 18D05.
Keywords: coherence, factorization algebra. 
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     author = {Robert Rosebrugh and R.J. Wood},
     title = {Coherence for {Factorization} {Algebras}},
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     publisher = {mathdoc},
     volume = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a5/}
}
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Robert Rosebrugh; R.J. Wood. Coherence for Factorization Algebras. Theory and applications of categories, Tome 10 (2002), pp. 134-147. http://geodesic.mathdoc.fr/item/TAC_2002_10_a5/