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Axiomatic Method and Category Theory
axiomatic method category theory geometry logic intuition structuralism
2016/5/27
Lawvere’s axiomatization of topos theory and Voevodsky’s axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory-building, which goes beyond the classical Hibert-style Axioma...
Category theory applied to a radically new but logically essential description of time and space
Category theory applied radically new logically essential description
2015/7/28
McTaggart's ideas on the unreality of time as expressed in "The Nature of Existence" have retained great interest for many years for scholars, academics and other philosophers. In this essay, there is...
Reconstructing Hilbert to Construct Category Theoretic Structuralism
Category theory mathematical structuralism Hilbert Shapiro
2009/9/16
This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to math...
Toward a Hermeneutic Categorical Mathematicsorwhy Category theory does not support mathematical structuralism
Category theory Hermeneutics Mathematics
2008/4/21
In this paper I argue that Category theory provides an alternative to Hilbert’s Formal Axiomatic method and doesn't support Mathematical Structuralism.
Complex Systems from the Perspective of Category Theory: I. Functioning of the Adjunction Concept
Complex Systems Information Structures Localization Systems
2008/4/10
We develop a category theoretical framework for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The fram...