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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorgregprice
   • CommentTimeJul 23rd 2022
   • PermaLink
   Author: gregprice
   Format: MarkdownItexCite Taylor's book, as taking the mentioned approach of teaching category-theoretic concepts first in the setting of orders. <a href="https://ncatlab.org/nlab/revision/diff/category+theory+vs+order+theory/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/category+theory+vs+order+theory/14">v14</a>, <a href="https://ncatlab.org/nlab/show/category+theory+vs+order+theory">current</a>

   Cite Taylor’s book, as taking the mentioned approach of teaching category-theoretic concepts first in the setting of orders.

   diff, v14, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 23rd 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexWasn't aware of this page (or I forget). Have added cross-linking with *[[relation between preorders and (0,1)-categories]]*. There is some overlap between the two entries, but maybe it doesn't hurt. <a href="https://ncatlab.org/nlab/revision/diff/category+theory+vs+order+theory/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/category+theory+vs+order+theory/16">v16</a>, <a href="https://ncatlab.org/nlab/show/category+theory+vs+order+theory">current</a>

   Wasn’t aware of this page (or I forget). Have added cross-linking with relation between preorders and (0,1)-categories. There is some overlap between the two entries, but maybe it doesn’t hurt.

   diff, v16, current

3. • CommentRowNumber3.
   • CommentAuthormaxsnew
   • CommentTimeJul 23rd 2022
   • (edited Jul 23rd 2022)
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexShouldn't the order-theory analogue of a groupoid be an equivalence relation?

   Shouldn’t the order-theory analogue of a groupoid be an equivalence relation?

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeJul 23rd 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexgroupoids (and dagger categories) are [[setoids]] in order theory. The equivalence relation is just the morphisms of the groupoid or dagger category.

   groupoids (and dagger categories) are setoids in order theory. The equivalence relation is just the morphisms of the groupoid or dagger category.

5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeJul 23rd 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexOne in general should distinguish between a binary endorelation (edge relation in graph theory), and the mathematical structure consisting of the binary endorelation and the carrier set (directed loop graphs in graph theory), just as one would a binary operation and a magma.

   One in general should distinguish between a binary endorelation (edge relation in graph theory), and the mathematical structure consisting of the binary endorelation and the carrier set (directed loop graphs in graph theory), just as one would a binary operation and a magma.