Author: BryceClarke Format: MarkdownItexCreated a new page on right-connected double categories, with a basic definition and reference. I intend to fill in with more details and examples soon.
<a href="https://ncatlab.org/nlab/revision/right-connected+double+category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Created a new page on right-connected double categories, with a basic definition and reference. I intend to fill in with more details and examples soon.
Author: BryceClarke Format: MarkdownItexAdded the definition of left-connected double category, and another example.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/3">v3</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Added the definition of left-connected double category, and another example.
Author: BryceClarke Format: MarkdownItexUnpacked the definition of a right-connected double category in explicit terms.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/4">v4</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Unpacked the definition of a right-connected double category in explicit terms.
Author: BryceClarke Format: MarkdownItexAdded a basic proposition that every right-connected double category admits a double functor to the double category of squares.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/5">v5</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Added a basic proposition that every right-connected double category admits a double functor to the double category of squares.
Author: BryceClarke Format: MarkdownItexAdded an Idea section, another basic example, and a new proposition stating the adjoint triple between the $2$-category of right-connected double categories and $Cat$.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/6">v6</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Added an Idea section, another basic example, and a new proposition stating the adjoint triple between the -category of right-connected double categories and .
Author: BryceClarke Format: MarkdownItexRearranged some content, added the example of monomorphisms and pullback squares, added more detail to several areas.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/8">v8</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Rearranged some content, added the example of monomorphisms and pullback squares, added more detail to several areas.
Author: BryceClarke Format: MarkdownItexAdded the "main theorem" which characterises those right-connected double categories which arise from algebraic weak factorisation systems. Also fixed some examples.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/9">v9</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Added the “main theorem” which characterises those right-connected double categories which arise from algebraic weak factorisation systems. Also fixed some examples.
Author: BryceClarke Format: MarkdownItexAdded several more examples, and two more basic properties: one characterising the thin right-connected double categories, and the other concerning orthogonal factorisation systems.
<a href="https://ncatlab.org/nlab/revision/diff/right-connected+double+category/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/right-connected+double+category/10">v10</a>, <a href="https://ncatlab.org/nlab/show/right-connected+double+category">current</a>
Added several more examples, and two more basic properties: one characterising the thin right-connected double categories, and the other concerning orthogonal factorisation systems.