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class
(unordered collection of objects, mathematical or not)
set
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An arrangement of mathematical(!) objects
(possible: several occurances of the same object):
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finite:
matrix
vector, tuple, ...
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-> represented by mappings
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On one set or between two sets:
connects objects pair-wise
(possible: same object can be connected multiply):
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graph
directed - cf. relation
labeled, ...
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relation
order, equivalence, ...
congruence (equivalence on algebra's set unseparable by algebra's operations)
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mapping/function
(maps objects in set A to objects in set B)
injection, surjection, bijection, ...
continuous, ...
functor (between the objects and arrows of two categories)
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-> represented by tuple sets
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A family of math.(?) objects ('arrows', 'morphisms')
connecting a group of math.(?) objects ('objects'):
closed under combinator o (kind of transitive):
category
function-composition closure of an algebra
some categories of relations [>]
some categories of algebras [>]
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set(s) with operations:
algebra
(family of functions, 'operations', on one set, or between/on several sets)
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geometrical object
2-d: point, line, triangle, square, polygon,
circle, ellipse, segment, ...
3-d: cube, cylinder, ...
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space
metric, Hilbert, ...
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Related symbolic objects:
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formula
(as in "symbolic" integration)
polynomes, (in)equations, eq. systems
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signature
(groups of function symbols and set symbols)
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