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Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this categorytheoretic treatment of concrete universals (...) 

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory and (...) 

Cognitive science depends on abstractions made from the complex reality of human behaviour. Cognitive scientists typically wish the abstractions in their theories to be universals, but seldom attend to the ontology of universals. Two sorts of universal, resulting from Galilean abstraction and materialist abstraction respectively, are available in the philosophical literature: the abstract universal—the oneovermany universal—is the universal conventionally employed by cognitive scientists; in contrast, a concrete universal is a material entity that can appear within the set of entities it (...) 

A cluster of similar trends emerging in separate fields of science and philosophy points to new opportunities to apply biosemiotic ideas as tools for conceptual integration in theoretical biology. I characterize these developments as the outcome of a “relational turn” in these disciplines. They signal a shift of attention away from objects and things and towards relational structures and processes. Increasingly sophisticated research technologies of molecular biology have generated an enormous quantity of experimental data, sparking a need for relational approaches (...) 

The use of mathematics in economics has been widely discussed. The philosophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a languagelike role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach. 

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this categorytheoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers (...) 