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The page defines the category of simplicial objects of the category of filters on sets. The category is flexible enough to formulate categorically a number of standard basic elementary definitions in various fields, e.g. in analysis, limit, (uniform) continuity and convergence, equicontinuity of sequences of functions; in algebraic topology, being locally trivial and geometric realisation; in geometry, quasi-isomorphism; in model theory, stability and simplicity of a theory.
Anonymous
The page defines the category of simplicial objects of the category of filters on sets. The category is flexible enough to formulate categorically a number of standard basic elementary definitions in various fields, e.g. in analysis, limit, (uniform) continuity and convergence, equicontinuity of sequences of functions; in algebraic topology, being locally trivial and geometric realisation; in geometry, quasi-isomorphism; in model theory, stability and simplicity of a theory.
Anonymous
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