Add to ORKGAbstract. We combine two recent ideas: cartesian differential categories, and restric-tion categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of Rn in a way that is completely algebraic. We also give other models for the resulting structure, discuss what it means for a partial map to be additive or linear, and show that differential restriction structure can be lifted through various completion operations
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifol...
Differential categories have a rich relation with proof theory and linear logic. In this talk, we wi...
AbstractWe determine explicit conditions on a category P which are equivalent to the request that it...
Restriction categories were introduced as a simple equational axiomatisation for categories of parti...
2 Cartesian restriction categories and objects of partial maps 6 2.1 Preliminaries on restriction ca...
AbstractGiven a category with a stable system of monics, one can form the corresponding category of ...
AbstractAn algebraic characterization of monads which are abstract partial map classifiers is provid...
A restriction category is an abstract formulation for a category of partial maps, defined in terms o...
axiomatization of categories of differentiable functions. The fundamental example is the category wh...
It is well known that one can build models of full higher-order dependent type theory (also called t...
Abstract. The construction of a free restriction category can be broken into two steps: the construc...
A 'Chen space' is a set X equipped with a collection of 'plots', i.e., maps from convex sets to X, s...
AbstractIt is well known that one can build models of full higher-order dependent-type theory (also ...
Empirical thesis.Bibliography: pages 95-96.1. Introduction -- 2. Cocompletion of restriction categor...
Introduction Partial maps are naturally ordered according to their extent of definition. Constructi...
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifol...
Differential categories have a rich relation with proof theory and linear logic. In this talk, we wi...
AbstractWe determine explicit conditions on a category P which are equivalent to the request that it...
Restriction categories were introduced as a simple equational axiomatisation for categories of parti...
2 Cartesian restriction categories and objects of partial maps 6 2.1 Preliminaries on restriction ca...
AbstractGiven a category with a stable system of monics, one can form the corresponding category of ...
AbstractAn algebraic characterization of monads which are abstract partial map classifiers is provid...
A restriction category is an abstract formulation for a category of partial maps, defined in terms o...
axiomatization of categories of differentiable functions. The fundamental example is the category wh...
It is well known that one can build models of full higher-order dependent type theory (also called t...
Abstract. The construction of a free restriction category can be broken into two steps: the construc...
A 'Chen space' is a set X equipped with a collection of 'plots', i.e., maps from convex sets to X, s...
AbstractIt is well known that one can build models of full higher-order dependent-type theory (also ...
Empirical thesis.Bibliography: pages 95-96.1. Introduction -- 2. Cocompletion of restriction categor...
Introduction Partial maps are naturally ordered according to their extent of definition. Constructi...
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifol...
Differential categories have a rich relation with proof theory and linear logic. In this talk, we wi...
AbstractWe determine explicit conditions on a category P which are equivalent to the request that it...