Accessible quasi-category¶
An infinity-category equivalent to the closure of a small infinity-category under kappa-filtered colimits for some regular cardinal kappa.
Core Idea¶
Accessibility is relative to some regular cardinal, accessible infinity-categories are typically large, small accessible cases are highly restricted and presentability adds existence of all small colimits. Kappa-compact objects form an essentially small generating subcategory and every object is reconstructed as a kappa-filtered colimit of those generators through an Ind-completion. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Accessible quasi-category belongs to higher category theory and is useful where the analyst can specify the typed higher category theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the infinity-category or quasi-category C, regular cardinal kappa, kappa-filtered colimits, kappa-compact objects, essentially small generating subcategory, equivalence with Ind-kappa of a small infinity-category, accessibility versus kappa-accessibility, accessible functors and relation to presentable and ordinary accessible categories are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the infinity-category or quasi-category C, regular cardinal kappa, kappa-filtered colimits, kappa-compact objects, essentially small generating subcategory, equivalence with Ind-kappa of a small infinity-category, accessibility versus kappa-accessibility, accessible functors and relation to presentable and ordinary accessible categories are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Accessible quasi-category. Accessible quasi-category compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed higher category theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the infinity-category or quasi-category C, regular cardinal kappa, kappa-filtered colimits, kappa-compact objects, essentially small generating subcategory, equivalence with Ind-kappa of a small infinity-category, accessibility versus kappa-accessibility, accessible functors and relation to presentable and ordinary accessible categories are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of higher category theory because they reuse the typed higher category theory carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Kappa-compact objects form an essentially small generating subcategory and every object is reconstructed as a kappa-filtered colimit of those generators through an Ind-completion., and type the carrier, state every parameter and convention in the definition, test that the infinity-category or quasi-category C, regular cardinal kappa, kappa-filtered colimits, kappa-compact objects, essentially small generating subcategory, equivalence with Ind-kappa of a small infinity-category, accessibility versus kappa-accessibility, accessible functors and relation to presentable and ordinary accessible categories are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Accessible quasi-category Domain-specific
Parents (1) — more general patterns this builds on
-
Accessible quasi-category is a kind of Aggregation Prime
The proposed strict upward parent is
prime:aggregation.
Hierarchy path (1) — routes to 1 parentless root
- Accessible quasi-category → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Accessible quasi-category sits in a crowded region of the domain-specific corpus (19th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Category-Theoretic Structures (79 abstractions)
Nearest neighbors
- Quasi-category — 0.92
- Ind-completion — 0.92
- Grothendieck category — 0.91
- Cartesian closed category — 0.91
- Subcategory — 0.91
Computed from structural-signature embeddings · 2026-09-08