On Concrete Universals: A Modern Treatment Using Category Theory

Concrete Universals in Category Theory

Category Theory and Set Theory as Theories about Complementary Types of Universals

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal uF = {x | F (...

On the Entanglement of Universals-Theory and Christian Faith in the Modern Theological Discourse of Karl Barth

The philosophical investigations into universals was entangled with the combination of a certain Christian faith and Ontology, especially in ancient and medieval times. That is, God’s creative activity provided us with the ontological presumption which enabled universals to be predicated, be perceived and be thought about. Times then have changed, and “the modern turn” in Philosophy tends to re...

Category Theory Using String Diagrams

In [Fokkinga, 1992a], [Fokkinga, 1992b] and [Fokkinga and Meertens, 1994] a calculational approach to category theory is developed. The scheme has many merits, but sacrifices useful type information in the move to an equational style of reasoning. By contrast, traditional proofs by diagram pasting retain the vital type information, but poorly express the reasoning and development of categorical...

Observations on Category Theory

1. Devised by Eilenberg and Mac Lane in the early 1940s, category theory is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger ...