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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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 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 sheaves 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.
   • CommentAuthorThomas Holder
   • CommentTimeJun 19th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexCreated an entry for this geometric theory. <a href="https://ncatlab.org/nlab/revision/theory+of+model+homomorphisms/1">v1</a>, <a href="https://ncatlab.org/nlab/show/theory+of+model+homomorphisms">current</a>

   Created an entry for this geometric theory.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeJun 21st 2020
   • PermaLink
   Author: IngoBlechschmidt
   Format: MarkdownItexThank you, Thomas! This geometric theory pops up in quite a few places: * It is what the topos constructed in [Fourman's reflection paper](https://link.springer.com/chapter/10.1007/978-3-642-39992-3_15) classifies. * It shows up in the [topos-theoretic Nullstellensatz](https://rawgit.com/iblech/internal-methods/master/slides-edinburgh2019.pdf). Unfortunately this week I'm very short on time, I hope that I can add to this entry next week!

   Thank you, Thomas! This geometric theory pops up in quite a few places:

   • It is what the topos constructed in Fourman’s reflection paper classifies.
   • It shows up in the topos-theoretic Nullstellensatz.

   Unfortunately this week I’m very short on time, I hope that I can add to this entry next week!

3. • CommentRowNumber3.
   • CommentAuthorThomas Holder
   • CommentTimeJun 24th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexAdded the classifying topos. Thanks to Ingo for the pointers! <a href="https://ncatlab.org/nlab/revision/diff/theory+of+model+homomorphisms/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/theory+of+model+homomorphisms/7">v7</a>, <a href="https://ncatlab.org/nlab/show/theory+of+model+homomorphisms">current</a>

   Added the classifying topos.

   Thanks to Ingo for the pointers!

   diff, v7, current

4. • CommentRowNumber4.
   • CommentAuthorThomas Holder
   • CommentTimeJul 6th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexAdded the generic morphism to the examples as well as a remark that assigning the twisted arrow categories to Grothendieck toposes is not a geometric theory functor. <a href="https://ncatlab.org/nlab/revision/diff/theory+of+model+homomorphisms/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/theory+of+model+homomorphisms/10">v10</a>, <a href="https://ncatlab.org/nlab/show/theory+of+model+homomorphisms">current</a>

   Added the generic morphism to the examples as well as a remark that assigning the twisted arrow categories to Grothendieck toposes is not a geometric theory functor.

   diff, v10, current

5. • CommentRowNumber5.
   • CommentAuthorThomas Holder
   • CommentTimeJul 10th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexGave the classifying topos for cartesian $T^2$ and started a section on the link to topos homotopy. <a href="https://ncatlab.org/nlab/revision/diff/theory+of+model+homomorphisms/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/theory+of+model+homomorphisms/15">v15</a>, <a href="https://ncatlab.org/nlab/show/theory+of+model+homomorphisms">current</a>

   Gave the classifying topos for cartesian $T^2$ and started a section on the link to topos homotopy.

   diff, v15, current