Research output: Working paper › Preprint
Research output: Working paper › Preprint
}
TY - UNPB
T1 - A survey of congruences and quotients of partially ordered sets
AU - Williams, Nicholas J.
N1 - 45 pages (39 pages excluding references), 8 figures, 1 table. Comments very welcome. v2: added references and new example to example section
PY - 2023/3/7
Y1 - 2023/3/7
N2 - The literature on congruences and quotients of partially ordered sets contains a large and profilerating array of approaches, but little in the way of systematic exposition and examination of the subject. We seek to rectify this by surveying the different approaches in the literature and providing philosophical discussion on requirements for notions of congruences of posets. We advocate a pluralist approach which recognises that different types of congruence arise naturally in different mathematical situations. There are some notions of congruence which are very general, whilst others capture specific structure which often appears in examples. Indeed, we finish by giving several examples where quotients of posets appear naturally in mathematics.
AB - The literature on congruences and quotients of partially ordered sets contains a large and profilerating array of approaches, but little in the way of systematic exposition and examination of the subject. We seek to rectify this by surveying the different approaches in the literature and providing philosophical discussion on requirements for notions of congruences of posets. We advocate a pluralist approach which recognises that different types of congruence arise naturally in different mathematical situations. There are some notions of congruence which are very general, whilst others capture specific structure which often appears in examples. Indeed, we finish by giving several examples where quotients of posets appear naturally in mathematics.
KW - math.CO
KW - math.HO
KW - 06-02, 06A06, 06A07, 06B10
M3 - Preprint
BT - A survey of congruences and quotients of partially ordered sets
ER -