Both symmetry and duality are important concepts, for sure; both conjure up images of "2-ness" (or 2-folded-ness or 2-sided-ness ...). However, their similarities and differences are problematic to me, and I'm seeking either agreement or objection from this forum to my remarks, plus a question on definition. An over-simplified picture (perhaps trivial) that begins to distinguish between these two fundamental aspects of 2-ness is the following: symmetry: . -----------> o o . -----------> ie. confluence vs. duality . ----------> o o . <----------- ie. unity of opposites "Symmetry is a vast subject, significant in art and nature" said Hermann Weyl in his 1952 Princeton UP book "Symmetry". As is well known, his mathematical approach culminates in the understanding of symmetric configurations of elements as invariants under subgroups of the group of automorphisms of their ambient structures. This, of course, relates strongly to the famous Erlanger Program (1872) of Felix Klein which sees geometry as the study of the properties of a space that are preserved (invariant) under a given group of transformations, whereby a geometry is distinguished by the group of transformations under which its theorems remain true. Duality is also a very important and far-reaching subject - and certainly no need to recite further in this forum. In terms of comparisons of similarities and differences, I am tempted to attach the follow descriptions: symmetry .......... vs. ............. duality ........2-ness................................2-ness .. metric (or measure) related........order related ... visual................................complementary ..... causal parallel......................dialectic .... syntactic..............................syntactic .... concrete..................................abstract .. invariance under transformation.....adjointness .. geometric in character...........algebraic in character ... confluence..........................unity of opposites .... are there others that come to mind? In the vernacular, symmetry and duality are sometimes used interchangeably, both referring to 2-ness: the quality, character or condition of being two or twofold - a dichotomy. Indeed it has been suggested that visual symmetry, in the sense of exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis, is a source of beauty as a result of this balance or harmonious arrangement. Alternatively, symmetry has also been seen more abstractly (vs. visually) as a relationship of equivalence, identity, or characteristic correspondence among constituents of an entity or between different entities, such as in: the narrative symmetry of a novel. This level of abstraction is certainly evident in the philosophical "Mind Body Problem" whose classical exposition in the form of dualistic interactionism is due to René Descartes. Both symmetry and duality should be seen as sources of beauty in mathematics also, however, in order to be addressed mathematically. these should be precise. The categorical notion of duality is captured precisely by adjointness, or the unity and identity of opposites. So finally, here is the question: is there a (universal) categorical description of symmetry? My hope is that precise formulations will allow me to better understand heuristic notions such as wave-particle duality or symmetry-breaking etc. in terms of (model) structures. Thank you for your kind attention. Al Vilcius personal: al.r@vilcius.com business: avilcius@webpearls.com