The Coherence Theorem for Ann-Categories
| dc.creator | Quang, Nguyen Tien | |
| dc.date | 2007-08-03 | |
| dc.date.accessioned | 2026-07-07T08:22:13Z | |
| dc.date.available | 2026-07-07T08:22:13Z | |
| dc.description | This paper presents the proof of the coherence theorem for Ann-categories whose set of axioms and original basic properties were given in [9]. Let $$\A=(\A,{\Ah},c,(0,g,d),a,(1,l,r),{\Lh},{\Rh})$$ be an Ann-category. The coherence theorem states that in the category $ \A$, any morphism built from the above isomorphisms and the identification by composition and the two operations $\tx$, $\ts$ only depends on its source and its target. The first coherence theorems were built for monoidal and symmetric monoidal categories by Mac Lane [7]. After that, as shown in the References, there are many results relating to the coherence problem for certain classes of categories. For Ann-categories, applying Hoang Xuan Sinh's ideas used for Gr-categories in [2], the proof of the coherence theorem is constructed by faithfully ``embedding'' each arbitrary Ann-category into a quite strict Ann-category. Here, a {\it quite strict} Ann-categogy is an Ann-category whose all constraints are strict, except for the commutativity and left distributivity ones. This paper is the work continuing from [9]. If there is no explanation, the terminologies and notations in this paper mean as in [9]. | |
| dc.description | 10 peges | |
| dc.identifier | https://arxiv.org/abs/0708.0592 | |
| dc.identifier | http://arxiv.org/abs/0708.0592 | |
| dc.identifier | (in Vietnamese) Vietnam Journal of Mathematics Vol. XVI, No 1, 1988 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135577 | |
| dc.subject | Category Theory | |
| dc.subject | 18D10 | |
| dc.title | The Coherence Theorem for Ann-Categories | |
| dc.type | text |