• Corpus ID: 14024710

Balanced category theory

@article{Pisani2008BalancedCT,
  title={Balanced category theory},
  author={Claudio Pisani},
  journal={arXiv: Category Theory},
  year={2008}
}
  • C. Pisani
  • Published 5 February 2008
  • Mathematics
  • arXiv: Category Theory
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this axiomatization of final and initial functors and discrete (op)fibrations, concepts such as components, slices and coslices, colimits and limits, left and right adjunctible maps, dense maps and arrow intervals, can be naturally defined in $\C$, and several… 
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References

SHOWING 1-10 OF 24 REFERENCES
Categories of categories
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those
The Category of Categories as a Foundation for Mathematics
In the mathematical development of recent decades one sees clearly the rise of the conviction that the relevant properties of mathematical objects are those which can be stated in terms of their
TOPOLOGY IN A CATEGORY: COMPACTNESS
In a category with a subobject structure and a closure operator, we provide a categorical theory of compactness and perfectness which yields a number of classical results of general topology as
The comprehensive factorization of a functor
In this article we show that every functor has a factorization into an initial functor followed by a discrete O-fibration and that this factorization is functorial. Size considerations will be
Handbook Of Categorical Algebra 1 Basic Category Theory
Category theory is the key to a clear presentation of modern abstract "Basic Category Theory for Computer Scientists" by Benjamin C. Pierce (1991). "Handbook of Categorical Algebra" by Francis
A categorical guide to separation, compactness and perfectness.
Based on a rather arbitrary class of morphisms in a category, which play the role of “closed maps”, we present a general approach to separation and compactness, both at the object and the morphism
Unity and identity of opposites in calculus and physics
TLDR
The description in engineering mechanics of continuous bodies that can undergo cracking is clarified by an example involving lattices, raising a new questions about the foundations of topology.
ON FUNCTORS WHICH ARE LAX EPIMORPHISMS
We show that lax epimorphisms in the category Cat are precisely the functors P : E −→ B for which the functor P ∗ :( B, Set) −→ (E, Set) of composition with P is fully faithful. We present two other
COMPONENTS, COMPLEMENTS AND THE REFLECTION FORMULA
We illustrate the formula (#p)x = !(x/p), which gives the reflection #p of a category p : P ! X over X in discrete fibrations. One of its proofs is based on a "complement operator" which takes a
The convergence approach to exponentiable maps.
Exponentiable maps in the category Top of topological spaces are characterized by an easy ultrafilter-interpolation property, in generalization of a recent result by Pisani for spaces. From this
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