Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories Export

@article{citeulike:1818518, abstract = {This paper presents indexed categories which model uniformly defined families of categories, and suggests that they are a useful tool for the working computer scientist. An indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms. Similarly, an indexed functor (which is a uniform family of functors between the components categories) induces a flattened functor between the corresponding flattened categories. Under certain assumptions, flattened categories are (co)complete if all their components are, and flattened functors have left adjoints if all their components do. Several examples are given. Although this paper is Part 3 of the series "Some fundamental algebraic tools for the semantics of computation", it is entirely independent of Parts 1 and 2.}, author = {Tarlecki, Andrzej and Burstall, Rod M. and Goguen, Joseph A.}, citeulike-article-id = {1818518}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0304-3975(91)90085-G}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/0304-3975(91)90085-G}, citeulike-linkout-2 = {http://www.sciencedirect.com/science/article/B6V1G-45FC3YT-S/2/201cc8c9980643d58ca7e3faa56df371}, day = {23}, doi = {10.1016/0304-3975(91)90085-G}, journal = {Theoretical Computer Science}, keywords = {algebraic-specification, institution}, month = {December}, number = {2}, pages = {239--264}, posted-at = {2008-10-30 07:21:16}, priority = {2}, title = {Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories}, url = {http://dx.doi.org/10.1016/0304-3975(91)90085-G}, volume = {91}, year = {1991} }

TY - JOUR ID - citeulike:1818518 L3 - citeulike-article-id:1818518 N2 - This paper presents indexed categories which model uniformly defined families of categories, and suggests that they are a useful tool for the working computer scientist. An indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms. Similarly, an indexed functor (which is a uniform family of functors between the components categories) induces a flattened functor between the corresponding flattened categories. Under certain assumptions, flattened categories are (co)complete if all their components are, and flattened functors have left adjoints if all their components do. Several examples are given. Although this paper is Part 3 of the series "Some fundamental algebraic tools for the semantics of computation", it is entirely independent of Parts 1 and 2. IS - 2 JF - Theoretical Computer Science EP - 264 TI - Some fundamental algebraic tools for the semantics of computation: Part 3. indexed categories VL - 91 SP - 239 KW - algebraic-specification KW - institution AU - Tarlecki, Andrzej AU - Burstall, Rod AU - Goguen, Joseph PY - 1991/12/23/ UR - http://dx.doi.org/10.1016/0304-3975(91)90085-G ER -