Morphism
A morphism is a structure-preserving arrow from one object to another; composing morphisms is the heart of category theory.
At a glance
Key signals
0% cross fields · reaches 2 more
- Category Theory
- Mathematics
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
System context
Morphismis part ofCategoryEstablished
Morphisms are the arrows of a category.
Mechanism: A category is defined by its objects and the composable morphisms between them.
Morphismis part ofCategoryEstablished
Morphism is a part of Category.
Isomorphismis aMorphismEstablished
Isomorphism is a kind of Morphism.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no verified source · no key date stored · 4 of 4 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 4 → 17 → 47 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 4 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
4 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Category, Category and Isomorphism.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Concepts
explicitly analogous
- Connects 4 other ideas across 2 disciplines.
- A cross-disciplinary bridge — its connections reach into 2 other fields.
- Most of its connections are of the “Kind & structure” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
No primary source is attached to this concept yet. In a real deployment this would be required before publication.