functorialityProperty
P29147
predicate
Indicates that a mapping between categories preserves the structure of composition and identity morphisms, behaving consistently with the rules of a functor.
All labels observed (11)
| Label | Occurrences |
|---|---|
| functoriality | 10 |
| isFunctorialIn | 3 |
| functorialIn | 2 |
| hasFunctoriality | 2 |
| isFunctorial | 2 |
| functorialUnder | 1 |
| functorialWithRespectTo | 1 |
| functorialityProperty canonical | 1 |
| isFunctorialFor | 1 |
| isFunctorialWithRespectTo | 1 |
| morphismsPreserveAddition | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: functorialityProperty
Generated description
Indicates that a mapping between categories preserves the structure of composition and identity morphisms, behaving consistently with the rules of a functor.
Sample triples (25)
| Subject | Object |
|---|---|
| Conway polynomial | invariant under ambient isotopy ⓘ |
| Lie ring | true via predicate surface "morphismsPreserveAddition" ⓘ |
| Fitting ideal | yes via predicate surface "isFunctorial" ⓘ |
| Whitney sum | true via predicate surface "isFunctorial" ⓘ |
| Todd class | holomorphic maps via predicate surface "isFunctorialFor" ⓘ |
| Henselization | defines a functor from local rings to Henselian local rings via predicate surface "functoriality" ⓘ |
|
Dolbeault cohomology classes
surface form:
Dolbeault cohomology class
|
holomorphic maps of complex manifolds via predicate surface "functorialIn" ⓘ |
|
Sullivan minimal model in rational homotopy theory
surface form:
Sullivan minimal model
|
topological spaces (up to homotopy) via predicate surface "isFunctorialIn" ⓘ |
| Kronecker pairing | topological space X via predicate surface "isFunctorialIn" ⓘ |
| Euler class | pullback of bundles via predicate surface "functorialUnder" ⓘ |
| Jacobson radical | homomorphic image of J(R) is contained in J(S) for ring homomorphism R→S via predicate surface "functoriality" ⓘ |
| Khovanov homology | link cobordisms via predicate surface "functorialWithRespectTo" ⓘ |
| HOMFLY-PT homology | invariant under Reidemeister moves via predicate surface "functoriality" ⓘ |
| Witt group of quadratic forms | contravariant in field homomorphisms via predicate surface "hasFunctoriality" ⓘ |
| Witt group of quadratic forms | covariant for field extensions via scalar extension via predicate surface "hasFunctoriality" ⓘ |
| Stiefel–Whitney classes | natural with respect to bundle maps via predicate surface "functoriality" ⓘ |
| Stiefel–Whitney classes | natural with respect to continuous maps of base spaces via predicate surface "functoriality" ⓘ |
| Frobenius endomorphism | morphisms of schemes over fields of characteristic p via predicate surface "isFunctorialWithRespectTo" ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
morphisms of curves via predicate surface "functorialIn" ⓘ |
| Picard group | contravariant in the scheme: a morphism f:Y→X induces f* : Pic(X) → Pic(Y) via predicate surface "functoriality" ⓘ |
| Beilinson spectral sequence | functorial in morphisms of coherent sheaves via predicate surface "functoriality" ⓘ |
| Chow groups | covariant for proper morphisms via predicate surface "functoriality" ⓘ |
| Chow groups | contravariant for flat morphisms via predicate surface "functoriality" ⓘ |
| Chow groups | contravariant for l.c.i. morphisms via predicate surface "functoriality" ⓘ |
|
Whitehead groups
surface form:
Whitehead group
|
group homomorphisms via predicate surface "isFunctorialIn" ⓘ |