- The topos theoretic foundations of computation are defined in terms of Sets and Sets^{\to}. An abstraction layer over that is provided by set relations and flow models. This new version contains a new and complete implementation of this fundamental research into the foundations of computation. At the same time you can get the lattice of subobjects of a set relation by calling the sub multimethod.
- We provide an implementation of relational functors which are functors of the form F : C \to Rel and several techniques for dealing with them. In particular, an algorithm is provided for converting a family of disets into a relational functor over the two arrow category.
- Support for partial transformation semigroups, such as the action by atomic charts of a preorder is provided. The action of a partial transformation semigroup is defined by a relational functor, with partial transformations described as set relations
- The conversion of morphisms of functions into copresheaves is defined basically based upon the presence of identities in either the input or output function. As a result, a morphism of functions could be presented as a triangle copresheaf if one of the two functions is an identity. This makes for a more pleasant experience with the copresheaf viewer.
- I wrote a function for creating module categories, defined as enriched categories with each hom class being an additive group. At the same time, the category of set relations is described as a 2-category with each hom class being a poset.
- I wrote a new function for converting topological spaces into sites. This will be useful when we further develop our Grothendeick topos theory subsystem.
- Half the functionality of the Locus project was moved into the elementary folder, dealing strictly with elementary topoi of copresheaves. This will make the project more organized when I add support for some things related to grothendeick toposes and schemes.
Friday, April 1, 2022
Locus 0.81 changes
In order to further develop the new elementary topos theoretic foundations of computation, I have produced a new version of the Locus project. Here are some of the changes.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment