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BASIC CONCEPTS OF ENRICHED CATEGORY THEORY
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES
, 2005
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Category Theory
"... Formalisation of some of the concepts of category theory in ProofPowerHOL. Created 2006/04/09 ..."
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Formalisation of some of the concepts of category theory in ProofPowerHOL. Created 2006/04/09
Category Theory
, 2013
"... This article presents a development of Category Theory in Isabelle. A Category is defined using records and locales in Isabelle/HOL. Functors and Natural Transformations are also defined. The main result that has been formalized is that the Yoneda functor is a full and faithful embedding. We also fo ..."
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This article presents a development of Category Theory in Isabelle. A Category is defined using records and locales in Isabelle/HOL. Functors and Natural Transformations are also defined. The main result that has been formalized is that the Yoneda functor is a full and faithful embedding. We also
Category Theory as the Language of Consciousness
"... Abstract. A form of Category theory with Grothendieck topologies is utilized to provide a preliminary mathematical formalism allowing the mathematical interpretation of the ideas of the principles of a conscious universe. Category theory is the most generalized form of mathematics and as such is sho ..."
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Abstract. A form of Category theory with Grothendieck topologies is utilized to provide a preliminary mathematical formalism allowing the mathematical interpretation of the ideas of the principles of a conscious universe. Category theory is the most generalized form of mathematics
SET THEORY FOR CATEGORY THEORY
, 2008
"... Questions of settheoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical constructio ..."
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Questions of settheoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical
Category theory for linear logicians
 Linear Logic in Computer Science
, 2004
"... This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categori ..."
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This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed
ASPECTS OF CATEGORY THEORY
"... I give a very brief introduction to category theory. The paper covers the basic definitions, some important basic constructions and spends some time discussing the important notion of categorical trace that has recently found many applications in computer science and the proof theory of Linear Logic ..."
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I give a very brief introduction to category theory. The paper covers the basic definitions, some important basic constructions and spends some time discussing the important notion of categorical trace that has recently found many applications in computer science and the proof theory of Linear
Category theory on the computer
"... Formalized mathematics have met an increasing interest in the last years. They give a way to build digital searchable libraries of mathematics, and computerverified proofs allow for a level of trust in the theory which the pen and paper versions cannot supply. Our goal is to build a library of categ ..."
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of category theory [2] in the proof assistent COQ [1]. It makes extensive use of modern features of COQ, such as type classes and generalized rewriting. 1.
WOMP 2004: CATEGORY THEORY
"... is not really an area of mathematics so much as an area of metamathematics. It describes frameworks in which mathematics can be, and usually is, done. More than that, in many cases category theory has encouraged, or at least facilitated, a change of perspective. When one studies mathematics, one of ..."
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is not really an area of mathematics so much as an area of metamathematics. It describes frameworks in which mathematics can be, and usually is, done. More than that, in many cases category theory has encouraged, or at least facilitated, a change of perspective. When one studies mathematics, one
Frames in Category Theory
"... This talk gives a representation of frames in category theory. All of the constituents of a frame — from the underlying universe of objects with thei attributes to the frame itself including constraints on its values — can be expressed in categories. Categories are employed in mathematics to regard ..."
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This talk gives a representation of frames in category theory. All of the constituents of a frame — from the underlying universe of objects with thei attributes to the frame itself including constraints on its values — can be expressed in categories. Categories are employed in mathematics to regard
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