id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_xikbmrhzg5eedbo65njok5nldy	Thomas William Barrett	What Do Symmetries Tell Us about Structure?	2018	18	.pdf	application/pdf	8181	703	68	There is a famous idea about the relationship between the symmetries, or automorphisms, of a mathematical object and the structure of the object: An of the mathematical object suffices to define the piece of invariant structure. Symmetries would then provide us with insight into a mathematical object's constitution because they tell us precisely which structures the is definable from the basic structure of a mathematical object, then it is invariant not provide us with a complete guide to the definable structures of the object. necessarily imply that it is definable from the object's basic structure. A piece of structure is invariant under the symmetries of a mathematical object if and only if it is definable from the basic structure of the object. A piece of structure is invariant under the symmetries of a mathematical object if and only if it is definable from the basic structure of the object.	./cache/work_xikbmrhzg5eedbo65njok5nldy.pdf	./txt/work_xikbmrhzg5eedbo65njok5nldy.txt