# Balanced category theory

@article{Pisani2008BalancedCT, title={Balanced category theory}, author={Claudio Pisani}, journal={arXiv: Category Theory}, year={2008} }

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…

## 3 Citations

A LOGIC FOR CATEGORIES

- Mathematics, Philosophy
- 2010

We present a doctrinal approach to category theory, obtained by abstract- ing from the indexed inclusion (via discrete brations and opbrations) of left and of right actions of X 2 Cat in categories…

Grothendieck topologies from unique factorisation systems

- Mathematics
- 2009

This work presents a way to associate a Grothendieck site structure to a (locally presentable) category endowed with a unique factorisation system of its arrows. In particular this recovers the…

A note on the Penon definition of $n$-category

- Mathematics
- 2009

We show that doubly degenerate Penon tricategories give symmetric rather than braided monoidal categories. We prove that Penon tricategories cannot give all tricategories, but we show that a slightly…

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